The American, an understudy to Brad Friedel at club and international level, saved Kenwyne Jones' late penalty to take the game to extra-time and ultimately penalties.
And he maintained his excellence by saving three of Sunderland's four spot-kicks in the shoot-out with Ashley Young converting the clincher to send Villa into the last eight.
The Wearsiders will feel hard done by but they only have themselves to blame after squandering some gilt-edged chances, none more presentable than that which fell to Kieran Richardson in the closing minutes of the extra period.
Having burst clean through, the former Manchester United midfielder should have scored but hammered his shot straight into the chest of Guzan.
The Villa stopper then saved Sunderland's first two spot-kicks, from Andy Reid and Lorik Cana, and although Gabriel Agbonlahor missed for the visitors, Guzan denied Jordan Henderson to secure victory for Martin O'Neill's men.