Rovers’ new number nine saw his first half spot kick saved by Will Norris but later capped another hard-working display by heading home Matty Blair’s sublime cross.
Marquis’s unrelenting work ethic epitomised a much livelier display from Rovers as they provided the perfect response to Saturday’s hugely underwhelming performance against Crawley Town.
Rovers had to survive a nervy end to the game as Andy Butler made a vital goal-line clearance to keep out Conor Newton inside 13 minutes of time added on - the result of a long delay after the lineswoman was taken ill.
But a Cambridge equaliser would have been unjust on a night when Rovers dominated and dictated play for the most part.
Darren Ferguson continued his ruthless selection policy as Ross Etheridge paid the price for his mistake against Crawley and was dropped for Marko Marosi. Tyler Garratt also replaced the injured Niall Mason, while Mitchell Lund came in for Riccardo Calder - changes which saw 3-5-2 ditched in favour of a 4-4-2 midfield diamond.
Rovers’ back four were nearly caught cold inside 40 seconds when a ball over the top picked out Ben Williamson but the lone striker’s effort went just wide.
The home side were handed the perfect chance to seize the initiative on nine minutes when Marquis was hauled down in the box by Sean Long and Darren Handley had no hesitation in pointing to the spot.
Marquis replaced Andy Williams on penalties, following his strike partner’s miss at Accrington, but suffered the same fate as his kick, aimed straight down the middle, was kept out by the legs of Cambridge goalkeeper Will Norris.
Ferguson was a very animated figure in the technical area, demanding tempo and purpose from his team, and they responded with three quickfire attempts just before the half hour.
First Williams saw his glancing header from Lund’s cross saved following an incisive move from one end to the other, before Norris had to be alert to stop shots from Marquis and Tommy Rowe.
Rovers had held the upper hand for the first 45 minutes and had shown a big improvement on the dire first half display at the weekend. All that was missing was a final product. Cambridge, meanwhile, had offered very little as an attacking threat.
There was more ruthlessness at the break from Ferguson as Garratt, somewhat tentative at left back, was replaced by Cedric Evina.
Rovers went agonisingly close to taking the lead shortly after the re-start when Williams burst into the box and pulled a great ball back for Marquis who saw two goal-bound efforts blocked before James Coppinger’s hooked volley was dealt with more comfortably by Norris.
After the lineswoman took ill Rovers again restarted the game in lively fashion - and soon grabbed the lead they deserved.
Some good defending at the near post deflected Marquis’ shot wide from Williams’ cross but the hardworking striker was not to be denied moments later when Blair picked him out with a sensational cross from the right and he headed home from close range.
Williams came close to doubling the lead and Tommy Rowe had a good case for a penalty when he turned in the box and appeared to have his shirt tugged.
Rovers then had Butler to thank for his late goal-line clearance during a nervy finish before the final whistle was greeted by a big outpouring of joy - and relief - from fans and players alike.
Rovers: Marosi, Lund, Wright, Butler, Garratt (Evina 46), Houghton, Blair, Coppinger, Rowe, Marquis, Williams. Subs not used: Etheridge, Mandeville, Middleton, Calder, Pugh, Fielding.
Cambridge: Norris, Long, Coulson, Dallison, Clark, Dunne (Piggott 79), Keane (Newton 75), Mingoia, Berry, Elito, Williamson. Subs not used: Gregory, Roberts, Legge, Adams, Taylor.
Referee: Darren Handley (Lancashire)