Both sides were committed to attack in a fast-paced match but Rovers always had the edge and could have won by a wider margin.
Defences stayed on top in an end-to-end first half, although Rovers should have gone in front when Lewis Guy was presented with a great chance in the 25th minute but his header finished wide of the mark.
Hartlepool found themselves on the defensive at the start with James Coppinger and Ricky Ravenhill both having early shots blocked.
Anthony Sweeney was denied by some excellent defensive work from Nick Fenton before Adam Boyd also had a shot deflected.
Top-scorer Boyd was generally well contained by the solid Rovers rearguard and Doncaster were close to scoring before the interval when Leo Fortune-West and Ravenhill went close in quick succession.
The turning point came early in the second half when Hartelpool missed their best chance of the match in the 57th minute and were quickly punished when Rovers went ahead.
Eifion Williams was the United culprit when he failed to capitalise on a golden opportunity created by Boyd.
He had cause to regret when Doncaster snatched the lead through Ravenhill after Guy had made amends for his earlier miss with a great run which set up the chance.
Guy and substitute Gregg Blundell went close to adding to the score before Michael McIndoe was denied by a save in the last minute.
Rovers underlined their superiority in injury time when Fortune-West pounced to force the ball home from close range following good work by Adam Brown and Paul Green.