With Wycombe Wanderers not playing until Monday, John Still's side had the chance to return to the summit with a win and Ricky Miller struck the decisive goal 20 minutes from time.
The 25-year-old striker fired home his first goal in the Football League to break the deadlock, a left-footed effort from outside the area good enough to beat Peter Brezovan.
Victory moves Luton - unbeaten in 11 - a point clear at the top, while Tranmere remain in the bottom two after a ninth loss of the campaign.
Shrewsbury Town are hot on Luton's heels after a sixth successive league win against Mansfield Town, pushing Wycombe down to third.
Micky Mellon's side had to wait until the 59th minute to open the scoring, with Bobby Grant on hand to steer a Jack Grimmer assist beyond Sascha Studer.
James Collins doubled Shrewsbury's lead with 15 minutes to play, ensuring their unbeaten home record in the league remains firmly intact.
Plymouth Argyle moved into fourth place with a thumping 3-0 win over Portsmouth, while Bury missed the chance to climb into the top three as they were beaten 1-0 by Morecambe.
Southend United occupy the final place in the top six thanks to a 1-0 win over rock-bottom Hartlepool United, David Worrall condemning the bottom club to another defeat.
Stevenage were the big winners on Saturday with a comprehensive 5-1 victory over Cheltenham Town as Graham Westley's side moved into the top half of the table.
Doubles from Chris Beardsley and Lee Barnard, plus Charlie Lee's fourth goal of the season, blew away Cheltenham, the visitors' only consolation being Byron Harrison's 76th-minute strike.
Oxford United moved seven points clear of the relegation zone with a 1-0 victory at York City, a defeat that sees Russell Wilcox's side slip to 21st place as Carlisle United were also able to win.
Derek Asamoah fired home the only goal of the game for Keith Curle's men as they beat Accrington Stanley 1-0, while AFC Wimbledon beat Dagenham and Redbridge by the same scoreline.
