Let's examine Paul's claim in its entirety. 

For there is no distinction; since all have sinned and fall short of the glory of God, they are justified by his grace as a gift, through the redemption which is in Christ Jesus, whom God put forward as an expiation by his blood, to be received by faith (Rom. 3:22b-25).

Paul talks specifically about all of humanity falling short and being in need of justification and redemption by the gift of grace, through the shedding of Christ's blood. The grace of God has a power to eradicate sin. (Grace and sin cannot occupy the same space. And that is how sinful folks like us may even consider this possibility of being glorified One Day in heaven.)

Further, Paul writes:

Therefore as sin came into the world through one man and death through sin, and so death spread to all men because all men sinned . . . (Rom. 5:12).

Everyone inherits Original Sin and its consequences. How does this apply to Mary?

The Church is not saying that Mary, a human person, was not in need of redemption. No, Mary is indeed redeemed by the merits of her Son, Jesus Christ -- remarkably redeemed, in fact!

But what the Church is saying, with the doctrine of the Immaculate Conception, reflecting on Luke 1:28, is that Mary received the first fruits of Christ's saving grace. Mary was redeemed by the merits of her Son Jesus at Calvary -- who is God -- at her conception.

Thus, Mary's sinless nature was like that of Eve's before the Fall.

Scripture scholars and theologians say Mary's role in salvation history was predicted all the way back in Genesis! You may recall after the Fall, as Adam and Eve lose their blessedness as punishment for their disobedience, a verse from Genesis 3 speaks of a woman to come:

I will put enmity between you and the woman, and between your seed and her seed; he shall bruise your head, and you shall bruise his heel (Gen. 3:15).

This is what is known as the proto evangelium -- the first good news -- found and foreshadowed in the Old Testament. The future victory over the serpent (a.k.a. evil or the devil) lies in the seed of the woman . . . that seed is pre-eminently the Christ. (cf. Gal. 3:16)

Following Christ's resurrection and ascension, Paul was quick to point out this continuity to the early church.

But when the time had fully come, God sent forth his Son, born of woman . . . (Gal. 4:4).

This is why Christian references about Mary throughout history have called her the "new Eve." And why St. Jerome (4th century) remarked: "Death through Eve, life through Mary."

From among the descendants of Eve, God chose the Virgin Mary to be the mother of his Son. "Full of grace," Mary is the most excellent fruit of redemption: from the first instant of her conception, she was totally preserved from the stain of original sin and she remained pure from all personal sin throughout her life. (Catechism of the Catholic Church, 508)

Mary was the first person redeemed by Jesus by an application of the grace, from his victory over sin and death on the Cross. This requires us to think expansively -- or bigger -- beyond our own sensibilities, as it were, to consider the mysteries of God's plan for salvation.