Rovers started the game in excellent style and looked more like the top-flight side than their opponents for the first 20 minutes.
They had a scare in the fourth minute when a mistake by Gareth Roberts allowed Gabriel Agbonlahor a chance, but the England striker fired just wide at the near post.
Doncaster had the upper hand after that enjoying more possession and playing the better football.
Their attacking intent was underlined when right back James O'Connor delivered a splendid cross in the seventh minute and left-back Roberts was up in attack to latch on to the ball and hammer just wide.
James Coppinger dribbled through on the edge of the box in the 20th minute to hit a powerful shot just over the bar and then Richie Wellens headed just over following a corner a couple of minutes later.
Doncaster had virtually outplayed their opponents up to that stage, but Villa began to get into the game just before half-time.
Rovers received a glimpse of the danger posed by their opponents when a super cross from Gareth Barry was headed just wide by James Milner in the 25th minute.
Neil Sullivan had to make an instinctive save to tip away a close-range effort by Agbonlahor in the 30th minute following a surging run from Nigel Reo-Coker.
But the home side finished the half strongly with Martin Woods unlucky to see a 20-yarder clip the top of the bar and bounce over, before John Spicer and Brian Stock had shots charged down following a corner.
Villa were much more prominent in the second half and Sullivan had to save at the foot of the post from Milner in the 60th minute, before Sam Hird cleared off the line from Agbonlahor three minutes later.
Agbonlahor missed a great chance to fire the visitors in front in the 71st minute when he raced clean through, but smacked his shot against the crossbar with only Sullivan to beat.
Rovers defended resolutely and finished strongly in the closing stages with Wellens charging through to fire just wide from 20 yards, before Woods hit a swerving free-kick against the post in the 87th minute.
Overall the draw was a fair result and the teams will have to do it all again at Villa Park.