Injury-ravaged Rovers were in desperate need of a victory after four successive Championship defeats had left them bottom of the table.
Veteran former England goalkeeper David James was in goal for City after groin trouble ruled out Dean Gerken.
Nicky Maynard wasted an early chance when he raced clear from halfway only sidefoot wide as Rovers goalkeeper Gary Woods came out to challenge.
Doncaster’s best chance came when John Oster poked a low cross goalwards but Lewin Nyatanga cleared.
Bristol went ahead in the 45th minute when Albert Adomah took a return pass from Marvin Elliott and burst past Tommy Spurr down the right of the area before sidefooting into the far corner.
Doncaster spurned a great chance to equalise when James beat away Jame Hayter’s 56th-minute spot-kick after Kyle Bennett had been tripped.
But Rovers would not be denied and the referee ruled Hayter’s 68th-minute header had crossed the line for the equaliser before being cleared.
In the end, Bristol were indebted to fine saves by James from Bennett and Simon Gillett for claiming a point.
O’Driscoll said: “That’s typical of James. There was no danger of him hiding after missing the penalty.
“He accepted responsibility when he took it in the first place and he was there when we needed him to head in the equaliser.
“I thought we handled the disappointments in the game very well. We gave a bad goal away and missed a spot-kick but we didn’t let it rattle us.
“We kept playing the right way and we gained our reward. It was a match we might have won but that’s been the case on more than one occasion this season so I’m thankful we got a point.”
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