The on-loan Plymouth winger fired in his fourth goal in five games after only seven minutes to keep the Dons in the play-off hunt, and they missed a host of chances to extend their lead.
Milton Keynes looked dangerous early on and Puncheon handed them the perfect start when he superbly swept home on-loan Tottenham winger Andros Townsend’s cross left-footed from 12 yards.
Townsend and Mathias Doumbe were then both narrowly off-target for the Dons before John Welsh blasted a 25-yard strike inches wide for Tranmere with keeper Wily Gueret well beaten.
Rovers goalkeeper Luke Daniels produced good saves after the break to keep out Aaron Wilbraham’s close-range flick and David McCracken’s header as the Dons continued to press.
The lively Townsend then curled just over the bar from the edge of the box before Dean Lewington’s header was cleared off the line.