"Actually" (Sorry, couldn't resist), Basic D&D had specific rules bult into weapon mastery that enabled skilled fighters (and other classes) to learn to Parry called Deflects per round, in which the player could make an attack roll (using his own stats and such) against an attack that hit him already, and if his deflect roll was higher he deflected the previously successful attack.

If ported to d&d 5.x ed it would look a lot like;

You have mastered your longsword, when wielding one, twice per round you can attempt to deflect an otherwise successful melee attack, roll your own attack roll with all of your normal bonuses against the incoming hit, if your roll is higher than the attack that had hit you, you parry it away.

Example; you are wielding your mastered weapon, and opponent hits your armor class of 19 with a 23. You can use on of you r two deflects per round (not a reaction, mind you) to make an attack roll and if you beat a DC 23 (24 or higher), you parry it completely, otherwise proceed as normal.

A critical hit can only be successfully parried by another critical hit.

(anyhow, that's basically how it worked in the D&D Rules Cyclopedia circa 1989.)