Heading into this clash at Prenton Park, Luton had lost their last seven games but had a chance to get back to winning ways when Rovers goalkeeper Peter Brezovan brought down Mark Cullen in the box with 10 minutes left.
Brezovan saved Cullen’s spot-kick, but Norwich loanee McGeehan reacted well to slot home the rebound for his second Luton goal to leave relegation-threatened Tranmere in the drop zone.
Tranmere could have gone ahead just four minutes in, with Steve Jennings putting Jennison Myrie-Williams through, but Hatters keeper Elliot Justham closed down well.
Luton’s only first half chance of note came as Paul Benson met Cullen’s cross from deep, forcing Brezovan to touch it wide.
There was concern for Rovers immediately in the first half as Max Power was taken off on a stretcher.
McGeehan’s strike followed, and Justham had to pull off a superb stop to earn his side the three points five minutes from time, acrobatically tipping substitute Marc Laird’s powerful header over the bar.