Veteran midfielder James Coppinger had given Rovers the lead midway through the first half when he rifled home following a scramble inside the box.
The match was delayed when Luton defender Scott Cuthbert was carried off on a stretcher, leading to 11 minutes of additional time in the first half.
By that point, however, Luton had reversed the scores with a quick-fire double.
Cameron McGeehan equalised with a neat finish at the back post before Jack Marriot slotted past the onrushing Marko Marosi five minutes before the break.
Any hopes of Doncaster maintaining their place in the automatic promotion places were exonerated when Joe Wright brought down Olly Pell inside the box, and McGeehan scored his second of the game from the spot.