But City fans endured a nervy finale after Steven Davis set up a grandstand finish with an 85th minute goal.
Stuart Pearce's side, inspired by the excellent Albert Riera, were deserved winners thanks to efforts from Georgios Samaras and Darius Vassell either side of half time.
For City, it will be a first appearance in the last eight of the FA Cup since 1993, while Villa will have to wait another season in their attempt to win the competition.
Both sides were hoping to set up a quarter-final tie with either West Ham United or Bolton Wanderers next Monday night.
City had the better of the opening period but it was Villa who created the first chance when a surging run by Davis set up Milan Baros. With keeper David James out of position, it needed Micah Richards, City's FA Cup hero from the first encounter, to block the effort.
Samaras then displayed good skill by turning the Villa defence on the edge of the penalty area but his shot was comfortably saved by Thomas Sorensen.
The striker also fired over the crossbar from Trevor Sinclair's cross as City built up a head of steam which eventually led to their opening goal.
Riera played a long ball inside full back Aaron Hughes to Samaras, who forced a decent stop from Sorensen. However, the rebound fell kindly to the feet of the Greek striker who gleefully stroked the ball home.
Richards denied Baros with an excellent sliding tackle after Richard Dunne had slipped on the touchline, but Villa's efforts to find an equaliser often ended with a misplaced pass.
City should have increased their lead six minutes before half-time but Sorensen saved brilliantly with his legs to deny Sinclair.
It took only three minutes of the second half for City to double their lead and the goal came after Villa had failed to clear a corner.
The ball fell to Riera on the edge of the penalty area and his first-time shot somehow find its way to Vassell who tapped home from three yards out with the Villa players looking to the assistant referee for an offside flag.
City should have made it 3-0 moments later but Antoine Sibierski headed against a post when unmarked.
Villa, needing a quick response, forced a couple of corners and were awarded a free-kick, but the opportunities were wasted.
A harsh handball offence against Riera provided Villa with a goalscoring chance but Gareth Barry sent the free-kick high and wide of James' upright.
The visitors, who were becoming increasingly desperate to reduce the deficit, were awarded a free-kick 20 yards from goal which Kevin Phillips forced James into punching away even though it seemed easier to catch the ball.
Sinclair sent a header wide from a Riera cross while at the other end Phillips was denied by Dunne's last-ditch block and Barry steered a shot wide of James' near post.
Villa did eventually pull a goal back when Davis slotted home from Luke Moore's pass but City held out for the remaining nine minutes to book their place in the next round.