Rovers produced some excellent football throughout and ultimately outplayed their illustrious opponents who looked dispirited at the finish.
Villa were never able to establish a foothold in the game and home keeper Dino Seremet never really had a serious shot to save as Doncaster cruised through to the quarter-finals for only the second time in their history.
David O'Leary's men looked menacing at the start with Milan Baros having an early volley saved, but they flattered to deceive as the game progressed.
Rovers gradually grew in confidence and began to take control of the game with Paul Heffernan and Lewis Guy both major threats in attack.
Michael McIndoe had an angled drive saved in the 12th minute and rolled another effort wide five minutes later before firing Rovers in front from the penalty spot.
Liam Ridgewell handled a driven cross from James Coppinger and McIndoe rattled home his eighth spot-kick of the season in the 20th minute.
Coppinger had a dipping shot saved and Heffernan had another effort cleared off the line as Doncaster remained on top for the rest of the half.
Villa came out after the break full of determination but were rocked again when Heffernan struck in the 53rd minute following good work by Dave Mulligan and Guy to put Rovers two up.
O'Leary's response was to send on former England man Kevin Phillips but it made no difference with Rovers in no mood to let their advantage slip.
McIndoe and Ricky Ravenhill both went close before Sean Thornton capped a brilliant Doncaster display with a stunning third goal from 20 yards in the 79th minute.
Villa could have no complaints about the result and finished well beaten as Rovers claimed their second Premiership scalp after knocking out Manchester City in an earlier round.