From my book: Bible Proofs for Catholic Truths (2009): available for only $2.99 as an e-book. All passages are KJV unless otherwise indicated. The words below are all from Scripture, excepting my notes or commentary in italics.
Deuteronomy 5:5: (I stood between the LORD and you at that time, to shew you the work of the LORD: for ye were afraid by reason of the fire, and went not up into the mount;)… (RSV: “to declare to you the word of the LORD”; Moses; cf. 1 Chron 15:15; 2 Chron 35:6)
1 Samuel 15:10: Then came the word of the LORD unto Samuel, saying, (cf. 1 Chron. 11:3)
2 Samuel 7:4: And it came to pass that night, that the word of the LORD came unto Nathan, saying, (cf. 1 Chron 17:3)
2 Samuel 23:2: The Spirit of the LORD spake by me, and his word was in my tongue. (King David: cf. 1 Chron. 22:8)
2 Samuel 24:11: For when David was up in the morning, the word of the LORD came unto the prophet Gad, David’s seer, saying,
1 Kings 6:11: And the word of the LORD came to Solomon, saying,
1 Kings 13:20-21: And it came to pass, as they sat at the table, that the word of the LORD came unto the prophet that brought him back:  And he cried unto the man of God that came from Judah, saying, Thus saith the LORD, Forasmuch as thou hast disobeyed the mouth of the LORD, and hast not kept the commandment which the LORD thy God commanded thee,
1 Kings 15:29: . . . according unto the saying of the LORD, which he spake by his servant Ahijah the Shilonite:
1 Kings 17:24: And the woman said to Elijah, Now by this I know that thou art a man of God, and that the word of the LORD in thy mouth is truth. (see also: 16:1, 7, 12 [Jehu]; 16:34 [Joshua]; 17:2, 8, 16 [Elijah]; 18:1 [Elijah] )
2 Kings 1:17: So he died according to the word of the LORD which Elijah had spoken . . .
2 Kings 7:1: Then Elisha said, Hear ye the word of the LORD; Thus saith the LORD . . .
2 Kings 9:36: Wherefore they came again, and told him. And he said, This is the word of the LORD, which he spake by his servant Elijah the Tishbite . . . (cf. 10:17)
2 Kings 14:25: . . . according to the word of the LORD God of Israel, which he spake by the hand of his servant Jonah, the son of Amittai, the prophet . . .
2 Kings 20:4: And it came to pass, afore Isaiah was gone out into the middle court, that the word of the LORD came to him, saying, (cf. 20:16, 19; 23:16)
2 Kings 24:2: . . . according to the word of the LORD, which he spake by his servants the prophets.
2 Chronicles 11:2: But the word of the LORD came to Shemaiah the man of God, saying, (cf. 12:7)
2 Chronicles 24:19-20: Yet he sent prophets to them, to bring them again unto the LORD; and they testified against them: but they would not give ear.  And the Spirit of God came upon Zechariah the son of Jehoiada the priest, which stood above the people, and said unto them, Thus saith God, Why transgress ye the commandments of the LORD, that ye cannot prosper? because ye have forsaken the LORD, he hath also forsaken you.
2 Chronicles 30:12: Also in Judah the hand of God was to give them one heart to do the commandment of the king and of the princes, by the word of the LORD.
2 Chronicles 36:21: To fulfil the word of the LORD by the mouth of Jeremiah . . . (cf. 36:22; Ezra 1:1; Jer. 1:2, 4; 2:4; 7:2; 13:3, 8; 14:1; 16:1; 18:5; 19:3; 21:11; 22:2, 29; 24:4; 28:12; 29:30; several more times in Jeremiah; Dan. 9:2)
Nehemiah 9:30: Yet many years didst thou forbear them, and testifiedst against them by thy spirit in thy prophets:… (RSV: “Many years thou didst bear with them, and didst warn them by thy Spirit through thy prophets”)
Isaiah 38:4: Then came the word of the LORD to Isaiah, saying, (cf. 39:5, 8; 66:5)
Jeremiah 25:3: From the thirteenth year of Josiah the son of Amon king of Judah, even unto this day, that is the three and twentieth year, the word of the LORD hath come unto me [Jeremiah], and I have spoken unto you, rising early and speaking; but ye have not hearkened.
Jeremiah 26:15: But know ye for certain, that if ye put me to death, ye shall surely bring innocent blood upon yourselves, and upon this city, and upon the inhabitants thereof: for of a truth the LORD hath sent me [Jeremiah] unto you to speak all these words in your ears.
Ezekiel 33:1: Again the word of the LORD came unto me [Ezekiel], saying,
“Word of the LORD” appears sixty times in the book of Ezekiel, usually in reference to the prophet Ezekiel.
Hosea 1:1: The word of the LORD that came unto Hosea . . . (cf. 4:1)
Joel 1:1: The word of the LORD that came to Joel the son of Pethuel.
Amos 7:16: Now therefore hear thou the word of the LORD . . .
Jonah 1:1: Now the word of the LORD came unto Jonah the son of Amittai, saying, (cf. 3:1, 3)
Micah 1:1: The word of the LORD that came to Micah . . .
Zephaniah 1:1: The word of the LORD which came unto Zephaniah . . .
Haggai 1:13: Then spake Haggai the LORD’s messenger in the LORD’s message unto the people, saying, I am with you, saith the LORD. (cf. 1:1, 3; 2:1, 10, 20)
Zechariah 1:1: . . . the word of the LORD unto Zechariah . . . (cf. 1:7; 6:9; 7:1, 4, 8; 8:1, 18)
Zechariah 7:12: Yea, they made their hearts as an adamant stone, lest they should hear the law, and the words which the LORD of hosts hath sent in his spirit by the former prophets: therefore came a great wrath from the LORD of hosts.
Malachi 1:1: The burden of the word of the LORD to Israel by Malachi.
Malachi 2:6-8: The law of truth was in his mouth, and iniquity was not found in his lips: he walked with me in peace and equity, and did turn many away from iniquity.  For the priest’s lips should keep knowledge, and they should seek the law at his mouth: for he is the messenger of the LORD of hosts.  But ye are departed out of the way; ye have caused many to stumble at the law; ye have corrupted the covenant of Levi, saith the LORD of hosts.
This passage is referring to Levites, who were teachers in Israel.
The prophets received their inspiration by the Holy Spirit (Num. 11:29; 2 Chron. 24:20; Neh. 9:30; Ezek. 3:24; 11:5; Zech. 7:12; Acts 28:25; 2 Pet. 1:21). The Holy Spirit (as a result of the New Covenant) is now given to all Christians (John 15:26; 1 Cor. 3:16), so it is perfectly possible and plausible that an even greater measure of the Holy Spirit would be given to leaders of the Church who have the responsibility to teach, since James wrote: “Let not many of you become teachers, my brethren, for you know that we who teach shall be judged with greater strictness” (James 3:1). The disciples were reassured by Jesus: “When the Spirit of truth comes, he will guide you into all the truth” (John 16:13; cf. 8:32, RSV), so surely it makes sense that shepherds of the Christian flock would be given an extra measure of protection in order to better fulfill their duties.
Jesus called John the Baptist “more than a prophet” (Luke 7:26, RSV) and stated, “among those born of women none is greater than John; yet he who is least in the kingdom of God is greater than he” (Luke 7:28, RSV). Therefore, it is not in the least implausible that one man: the pope, could be infallible, which is a far lesser gift than the inspiration and direct revelation from God exhibited by the prophets.
Briefly put, then, the argument is: “If prophets spoke with inspiration, then popes can plausibly speak infallibly, since the latter is a far less extraordinary gift than the former.” Or, from a different angle: “If those with lesser gifts can do the great thing (inspired utterance), then those with greater gifts can certainly do the lesser thing (infallible utterance).”
Matthew 1:22: Now all this was done, that it might be fulfilled which was spoken of the Lord by the prophet, saying, (cf. 2:15)
Luke 1:70: As he spake by the mouth of his holy prophets, which have been since the world began:
Acts 28:25: And when they agreed not among themselves, they departed, after that Paul had spoken one word, Well spake the Holy Ghost by Esaias the prophet unto our fathers,
2 Peter 1:21: For the prophecy came not in old time by the will of man: but holy men of God spake as they were moved by the Holy Ghost.
See further New Testament references to prophets and prophesying: Acts 2:16-18; 11:27-28; 13:1; 15:32; 19:6; 21:9-10; Rom. 12:6; 1 Cor. 11:4-5; 12:10, 28-29; 14:1, 3-6, 22, 24, 29, 31-32, 37, 39; Eph. 3:5; 4:11; 1 Thess. 5:20; 1 Tim. 1:18; 4:14).
Any non-Catholic Christian who believes in the inspiration of Holy Scripture, and who accepts the received canon of Scripture (either sixty-six or seventy-three books) — itself deriving from authoritative conciliar and papal pronouncements of an infallible Catholic Church — accepts the fact that St. Peter, the undisputed leader of the twelve disciples, and (we believe) the first pope, has written two inspired epistles (or proto-encyclicals). Inspiration means “God-breathed”: a positive characteristic that includes being entirely free from error (as all God-inspired words of revelation are truth).
Infallibility is a limited, far less profound “negative” protection against error. Everyone who holds to the inspiration of Scripture already believes that St. Peter wrote inspired words from God in the Bible. Where, then, is the inherent difficulty in believing that he and his successors could be protected by the Holy Spirit to write infallible documents (see, e.g., John 14:26; 15:26; 16:13; Acts 15:28)? The more difficult thing to believe, the thing that requires far more faith, since it is a greater gift, is already accepted, so what insuperable prima facie difficulty remains in the notion of infallible (as opposed to inspired) popes (and an infallible Church)?
(originally from 2009)