Ricky Miller’s first ever football league goal saw Luton climb to the top of the League Two table.
The 25-year-old striker’s left-footed curling strike extended the League Two side’s unbeaten league run to 11 games.
Both ‘keepers were called into action inside the first 20 minutes, with Luton’ stopper Mark Tyler making saves from Tranmere’s Armand Gnanduillet and Max Power’s respective efforts.
Mark Cullen had a shot saved from an acute angle by Peter Brezovan, low to his left.
Luton came closest to opening the scoring in the first half, in the form of Luke Guttridge as he volleyed a cross from Fraser Franks inside the six-yard box, only to be denied by a Brezovan finger tip.
Rovers made all the running in the opening stages of the second half, as Power had a right-footed shot saved and Danny Johnson had an attempt blocked.
In the 65th minute, manager John Still bought on match winner Miller, who netted five minutes after being introduced.
Miller finally broke the deadlock as he got the ball just outside the penalty area, opened up onto his left-foot and caressed the ball into the bottom left corner past Brezovan.
The Hatters came closest to adding to the scoreboard in the last minute, as Jake Howells rocket shot missed by millimetres.