Goals from Pelly-Ruddock Mpanzu, Danny Hylton, Kazenga LuaLua and Luke Berry handed Luton a deserved triumph that could so easily have come by an even wider margin.
Luton were energetic, smart and relentless to take the game to Rovers and not give them a minute in attack or defence.
But Rovers - undoubtedly hurting from the injury-related absences of key duo Ben Whiteman and Herbie Kane - were incredibly sloppy, arguably the poorest they have been in possession this season.
Rovers delivered the more threatening moments in a cagey opening with John Marquis superbly chasing down a kick out from goalkeeper James Shea and deflecting the ball narrowly wide.
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And Mallik Wilks cut inside but his trademark drive for the near post was a tame one and easily gathered by Shea.
But in terms of sustained periods, that was by far as good as it got for Rovers.
Luton grew into the game and were soon quickest to everything. They closed Rovers down in the middle of the park, both forcing errors and taking advantage of poor play.
Berry headed straight at Marko Marosi and it needed a big block from Paul Downing to deny Elliot Lee as the hosts pushed forward.
The hosts took the lead on 34 minutes when Mpanzu was given time and space to finish side footed from 15 yards into the bottom corner.
It took 12 minutes of the second half for the hosts to double their advantage.
Impressive full back Jack Stacey was given time to drive for the byline and cut a ball back which substitute Berry curled on goal only for Hylton to get the vital touch beyond Marosi.
And the game was wrapped up the game eight minutes from time.
Sweeping forward on the break, the ball was fed through to LuaLua who finished confidently beyond Marosi.
Unsurprisingly, there was still time for one more with Berry working space on the edge of the area before smashing a shot high into the goal.
With rivals Peterborough United beating Southend United, Rovers are out of the top six.
LUTON: Shea, Stacey, Bradley, Pearson, Potts (Berry 22); Mpanzu; Shinnie, Justin; Lee; Hylton (Cornick 79), LuaLua (Cummings 87). Subs not used: Isted, Moncur, Thorne, Sheehan.
ROVERS: Marosi; Lewis (Hasani 72), Downing, Butler, Andrew; Blair, Crawford, Rowe (Sadlier 63); Wilks (Smith 63), Marquis, Coppinger. Subs not used: Jones, Anderson, Beestin, May.
REFEREE: John Busby
ATTENDANCE: 10,071 (544 away)