Two goals in three minutes turned the game round after Scunthorpe had grabbed an early lead.
That came after 14 minutes when Jimmy Ryan curled in a cross from the right which found striker Karl Hawley, who steered his header from the edge of the six yard box into the far corner of the net past keeper Owain Fon Williams.
It was his first goal in six games since joining the club on a short-term contract.
It was also the fifth time in the last six games that Scunthorpe had taken an early lead.
They might have extended it, with winger Mark Duffy twice testing goalkeeper Owain Fon Williams with efforts from the edge of the box.
Tranmere were largely disappointing as an attacking force, their best effort coming on the stroke of half-time when Zoumana Bakayogo fired well off target after breaking into the box.
But they began to press more strongly after the interval and were rewarded with an equaliser after 63 minutes when a right wing corner from Adam McGurk was headed home by skipper James Wallace.
Two minutes later they struck again from another corner, this time forced home from close range by striker Jean-Louis Akpa Akpro for his sixth goal of the season.
And three minutes from time Akpo Akpro struck again after some shocking defending by the home side.