Goals from Georgios Samaras and Darius Vassell swept Manchester City into the FA Cup quarter-finals and a tie against either Bolton Wanderers or West Ham.
Samaras single-handedly unravelled the Villa defence on 17 minutes, scoring at the second attempt to put City ahead.
Ex-Villa forward Vassell picked up the striking baton for City on 48 minutes, turning the ball home after a scramble.
With five minutes left, Steve Davis' well-worked goal set up a tense finale, but it proved too little, too late.
City had forced a replay with a stoppage-time goal from Micah Richards, but their defence proved more adept at closing out a game than Villa's had back in February.
When he picked up the ball wide on the wing, there appeared little danger to the Villa defence.
But he cleverly flicked the ball past Olof Mellberg and raced into the Villa penalty area before getting in a shot that Sorensen was unable to hold.
The ball rebounded to the Greek, who rattled the ball into the net before wheeling away to celebrate.
Soon after breaking the deadlock, Samaras was the victim of an ugly challenge from Liam Ridgewell, who raked his studs down the striker's back.
Having survived that challenge, Samaras was withdrawn at the interval after coming off the worst following a tackle from Gareth Barry.
While City's attack prospered, Villa's frontmen struggled to get out of first gear.
The visitors had suffered a blow just before the kick-off when Patrik Berger, who had been planning to return for this game after a five-month absence, had to pull out after damaging his Achilles in the warm-up.
Villa's other Czech, Milan Baros, might have given David O'Leary's an early lead, but the former Liverpool striker was too slow to shoot after David James' had been left stranded following a rash dash out of his area.
Baros eventually went off injured five minutes before the break after he fell heavily following Richards' crunching tackle.
City extended their lead three minutes into the second-half after Villa failed to clear a corner.
When Albert Riera fired a shot into packed penalty area, Vassell, who scored twice against his former club in October, was on hand at the far post to turn the ball home.
Villa struggled to test James throughout most of the second half, but Davis fired a shot past the goalkeeper with five minutes left.
"I was so proud of my players - they were fantastic. All of them were outstanding.
"I thought we played pretty well when we did the things we're good at.
"There was a bit of pressure on us - people think being at home it was a foregone conclusion but it never is."
"I was very proud of the young lads, and the future of club is going to be good.
"They will learn from that, but we gave ourselves a lot to do."
Man City: James, Jihai, Dunne, Richards, Jordan, Sinclair, Barton, Musampa, Riera, Samaras (Sibierski 45), Vassell (Wright-Phillips 89).
Subs Not Used: Weaver, Sommeil, Reyna.
Booked: Samaras, Riera, Musampa.
Goals: Samaras 17, Vassell 49.
Aston Villa: Sorensen, Hughes, Mellberg, Ridgewell, Bouma, McCann, Davis, Barry, Baros (Gardner 40), Phillips, Moore.
Subs Not Used: Taylor, Samuel, Whittingham.
Booked: Gardner, Mellberg, McCann.
Goals: Davis 85.
Att: 33,006.
Ref: P Dowd (Staffordshire).