A deflected effort from Luke Young and a late Elliot Lee strike were the difference as Phil Parkinson’s side extended their unbeaten league run to six games.
Rovers’ wait for their first win of the season continues.
After a bright start from the home side, which saw Sam Dalby’s effort saved by Ian Lawlor, the visitors could have opened the scoring themselves through Mo Faal, while Tom Anderson blazed over from just six yards.
But it was Wrexham who took the lead in the 37th minute when Young’s effort was deflected past the helpless Lawlor in the Rovers goal after Ollie Palmer and Lee had come close moments earlier.
Doncaster continued to enjoy plenty of possession after the break and their pressure was rewarded when Faal headed home from a Joe Ironside cross.
Wrexham could have retaken the lead when Will Boyle’s header flashed wide and Palmer’s effort was saved by Lawlor, but it was Lee who stole the points with a thunderous drive from the edge of the box in the 88th minute.