Rovers secured their first victory under Valerien Ismael and a first league win at Luton following a resilient performance at Kenilworth Road.
Yuki Ohashi scored the decisive goal early in the second half after combining with Ryan Hedges in the final third.
Rovers had to play the last half hour with 10 men after Kristi Montgomery was sent off on his full debut but dug deep to get over the line.
Ismael made a couple of changes from the comeback against Sheffield Wednesday, with Balazs Toth selected in goal after Aynsley Pears picked up an Achilles injury.
Montgomery made his full debut, with Joe Rankin-Costello on the bench after he was forced off in midweek.
Montgomery was immediately called upon to block Millenic Alli’s shot after a flick-on by Carlton Morris, who was a nuisance for the backline from the off.
Ohashi sent an early strike over the bar after cutting onto his left foot, which turned out to be Rovers’ only effort on goal during the opening 45 minutes.
Alli had a big chance to open the scoring after Mark McGuinness’ knock down from a corner, but Toth made a smart stop from close range.
Thelo Aasgaard then caught a volley sweetly from the edge of the box but Danny Batth made the block.
McGuinness continued to look dangerous from set-pieces, sending a header just over the crossbar after getting on the end of Jordan Clark’s free kick.
Rovers started the second half brightly and took the lead through Ohashi, who latched onto Ryan Hedges’ pass and kept his cool to slot past Thomas Kaminski.
Moments later, Rovers were dealt a major blow with Montgomery sent off for a second booking in quick succession.
It was a heartbreaking end to his full Rovers debut and, in response, Ismael brought on Dion Sanderson for Todd Cantwell to shore up the backline.
Jordan Clark went for goal from the resulting corner but it wasn’t troubling Toth. Moments later, Aasgaard saw a strike from distance deflected over.
Aasgaard thought he had found an equaliser with a thumping strike from outside the box but the woodwork came to Rovers’ rescue.
Ismael’s side faced waves of pressure in the final stages but stood firm to bring all three points back to Lancashire, with Alli curling a cross-shot onto the woodwork in stoppage time.
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