The game looked like finishing goalless with both sides having cancelled each other out in a defence dominated clash.
But City were awarded a free kick in the 88th minute and McCombe rose high to plant a towering header into the roof of the net when Lee Johnson floated the ball into the penalty box.
It was rough luck on Doncaster whose own promotion play-off hopes now look doomed after matching the visitors for most of the game.
Rovers were lacking three key attackers and they failed to find the pay-off punch in front of goal after making a bright start.
Jonathan Forte and Bruce Dyer both failed to make the best of scoring opportunities inside the first 20 minutes.
City began to take charge after that with Stephen Brooker having a shot on the turn well saved in the 23rd minute before Kevin Betsy fired wide when he should have hit the target from 10 yards.
The visitors continued to take the game to Doncaster at the start of the second half with home skipper Graeme Lee having to produce a tremendous tackle to keep out Brooker after Adam Lockwood had given the ball away.
But Rovers rallied again and were unlucky not to score when Paul Green fired home in the 73rd minute only to have the effort disallowed for offside.
Brian Stock was outstanding in midfield for Doncaster and he headed just wide a minute later before Danny Cadamarteri had an angled volley well saved by Adriano Basso in the 82nd minute.
But it was City who grabbed the winner to send their large contingent of travelling fans wild with delight.