Rovers boss Sean O'Driscoll suggested after the first match ended goalless, that the replay could hinder their survival chances, but after four wins in five league games they have climbed away from the relegation zone.
O'Driscoll's players did not let him down. Despite Young dancing his way through the box and blazing over keeper Sullivan - and the bar - in the opening exchanges, Doncaster more than matched their Premier League counterparts for large portions of the match.
However, after 15 minutes the visitors defence crumbled.
Sullivan saved well from Gardner but he could only push the ball into the path of Sidwell, who poked in his fourth Villa goal since his move from Chelsea last summer.
The home crowd only had to wait five minutes before having another goal to cheer.
Carew picked up the ball on the edge of the box and his shot was deflected by defender Sam Hird into the top left corner over the stranded Sullivan.
Anybody thinking Doncaster would sit back and let the Premier League outfit spend the rest of the match having shooting practice was badly mistaken.
Midfielder Richie Wellens should have done much better from the edge of the box, and then in first half injury time they grabbed a well deserved lifeline.
James Coppinger crossed the ball into the box and picked out Price, and with Delfouneso flapping, he steered a low shot past Guzan into the corner of the net.
Both teams continued to press forward with Villa's Delfouneso and Gardner going close.
Just before the hour Rovers came within a finger nail of the equaliser. The impressive midfielder Stock pulled back the trigger from 30 yards but Guzan tipped the ball round the post.
It seemed to wake Villa up and Shorey burst forward to cross the ball in and a diving Delfouneso nodded into the top corner.
Doncaster, 37 places below Villa in the league standings, rarely threatened again but they can hold their heads up high after impressing in both matches.
Aston Villa boss Martin O'Neill:
"Doncaster played well but the important thing is that everybody can get some sort of football. We are getting there slowly.
"We have 14 Premier League games left. All players until the end of the season will have to step up to the mark. We will have injuries and suspensions so I just hope they are all ready."
Doncaster's goalscoring midfielder Jason Price:
"That's my first goal of the season. I've had chances all season but to score against Villa is unbelievable.
"I know we lost but it could have gone either way. We had a game plan and stuck to it. For the two goals we didn't mark and you can't do that against Premier League opposition. It's a learning curve for everybody."
Aston Villa: Guzan, Luke Young, Davies, Cuellar, Shorey, Gardner, Salifou, Sidwell, Ashley Young (Osbourne 78), Delfouneso, Carew.
Subs Not Used: Friedel, Barry, Milner, Agbonlahor, Knight, Lowry.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.