Rovers scored early in both halves to maintain their unbeaten league record at the Keepmoat.
Grant McCann’s troops remain seventh in the table and just behind sixth-placed Fleetwood on goal difference.
McCann made two alterations to the team which drew at table-topping Peterborough last week.
One of those changes, Matty Blair, was responsible for two sublime moments in the early throes of the game.
The utility man picked up the ball from the right, made inroads and then found the top-left corner with a superb strike to open the scoring on six minutes.
His somersault celebration to commemorate the goal was almost as impressive.
Rovers’ stopper Marko Marosi did well to keep out Jorge Grant’s dipping free-kick as the visitors pressed forward in search of an equaliser.
James Collins’ snapshot also drew a decent stop from the home ‘keeper as the visitors stepped up their pursuit.
Luton thought they had equalised on 33 minutes but the referee blew for a foul in the build-up to Matty Pearson bundling in from a corner.
But they didn’t have to wait long. Elliott Lee nodded in from a couple of yards out after a knock-down from a corner, in first half added time.
The heavens opened good and proper just as the second half began and the change in weather heralded a brighter outcome for Doncaster.
Less than a minute after the restart, Ben Whiteman lashed home a shot through a sea of bodies to restore Rovers’ lead.
Mallik Wilks lashed over moments after, whilst Danny Andrew’s curled effort just flashed wide.
Luton then soaked up the pressure and always looked a threat on the counter, and the impressive Pelly Ruddock-Mpanzu saw an effort from a tight angle deflected behind for a corner.
James Coppinger should have made it 3-1 to the hosts when slipped in on 70 minutes but the veteran slid a shot wide.
Luton pushed hard for a second leveller - Glen Rea poked wide in stoppage time - but despite their best efforts they couldn’t deny Rovers a third win of the campaign.
Doncaster Rovers: Marosi, Mason, Wright, Butler, Andrew, Whiteman, Kane (J Anderson 75), Coppinger (Taylor 81), Blair, Marquis, Wilks (May 62). Subs not used: Lawlor, T Anderson, Prior, Beestin
Luton Town: Shea, Bradley, Pearson, Potts, Stacey, Lee, Rea, Cornick, Ruddock-Mpanzu, Grant (Jarvis 85), Collins (O’Kane 76). Subs not used: Justin, McCormack, Shinnie, Isted, Sheehan
Referee: T Nield (W Yorks)