Substitute Craig Curran and Antony Kay turned out to be the heroes with goals in the 83rd and 86th minutes.
Luton often played the more accomplished football and led from the sixth minute. Paul Furlong headed home at the far post from a corner by David Bell.
Moments previously Furlong had seen a header from a Bell cross strike the bar.
Tranmere huffed and puffed to no avail. Steve Davies was unlucky with two good efforts, then Shane Sherriff saw a goalbound header headed off the line by Alan Goodall in the 33rd minute.
David Forde in the Hatters goal did well to push over a powerful angle shot by Davies straight after the restart.
But then it needed a fine diving save by Danny Coyne to deny Bell from the edge of the box.
It seemed Tranmere's luck was right out when Ben Chorley and Gareth Taylor missed their chances with the goal gaping and Chris Greenacre fired inches wide.
Manager Ronnie Moore sent on Curran in the 71st minute and Kay five minutes later and the reward was immense. Curran found a space in the 83rd minute to beat Forde from close range after Chorley pumped a long ball into the box.
Luton at the time were missing defender Richard Jackson, who was off the field having attention to a head injury.
The winner by Kay was a looping header from a free-kick by Davies.
Bell was superb for the losers and Steve Robinson also made his presence felt in midfield.
The visitors often produced the more accomplished football, but Tranmere's never-say-die attitude paid off in the end.
Davies was superb for the winners and there was also a lively contribution from Greenacre and Sherriff in a thoroughly entertaining encounter.
Kay picked up an unnecessary booking for his goal celebration. Bell was also unluckily cautioned after a clash with Davies in the 76th minute and he was then replaced in the closing stages.