Doncaster had the upper hand at the start but both teams were keen to play attractive attacking football despite the slippery conditions.
City survived appeals for a penalty in the 11th minute when Mickey Bell brought down Rovers new on loan striker Simon Johnson from behind and it looked like a justified appeal by the home players.
But Rovers pressed on undaunted with Neil Roberts firing over the top from 20 yards before Michael McIndoe cut inside to hit a low shot inches wide.
City enjoyed a spell of possession which was non productive and Bell chipped over the crossbar after Luke Wilkshire had set him up in the 30th minute.
But it was Doncaster who deservedly went in front following a 34th minute free-kick from Paul Green which was flicked on by McIndoe for Roberts to dart in and head home in fine style at the far post.
Tim Ryan dribbled past a couple of opponents to fire over the top a couple of minutes later before City equalised on the stroke of half time.
Rovers were made to pay for diving into the tackle on the halfway line and Wilkshire was made a present of the ball which he slipped to Steve Brooker who fired home from just inside the box.
Scott Murray hit the post with a 20 yarder in the 63rd minute before McIndoe missed a great chance from close range six minutes later as both sides pressed for all three points after the interval.
In a frantic finish Andy Warrington twice denied Brooker with splendid saves before John Doolan had a cracking 20 yarder parried by Steve Phillips two minutes from time.
City had a fortunate escape in the last minute when Roberts flashed a swerving shot wide after Johnson had set up the chance.