Tranmere moved level on points with AFC Wimbledon in League One after edging out their South London opponents 1-0 at Prenton Park.
Rushian Hepburn-Murphy scored the only goal midway through the first half but Rovers wasted a host of chances to put the game to bed and had to live dangerously until the very end.
The Merseysiders took the lead when Manny Monthe won a knockdown at the far post, allowing Connor Jennings to swivel and shoot at goal.
Nathan Trott kept his effort out and also clawed Hepburn-Murphy's rebound away but the linesman ruled that the ball had already crossed the line.
The Dons goalkeeper was single-handedly keeping the visitors in the contest after the break, denying Neil Danns and Hepburn-Murphy, with the latter also hitting the side-netting and blazing a great chance over the bar.
Jennings crashed another effort against the post but despite their profligacy in front of goal, Wimbledon offered little at the other end, handing Tranmere a crucial victory in the battle to avoid relegation.