A Bradley Dack double, sandwiched either side of Elliott Bennett's first goal of the season, ensured Rovers continued their surge at the top of table.
Dack's first was fairly fortunate, but his second was a touch of class, as he marked his return to the side with a strike in each half.
Bennett's belter for Rovers' second goal made things more comfortable for Tony Mowbray's side in freezing conditions in south London.
The cherry on the top of the cake was a first away clean sheet since November for David Raya, and Rovers will now head into Sunday's home battle against Wigan full of confidence after four consecutive victories.
Dack was back in attack, as Mowbray made one change to the starting XI for the midweek trip.
Dack returned to the lineup after missing out on the trip to Walsall on Saturday, and came in for Corry Evans.
Evans dropped to the bench, whilst Dominic Samuel missed out on the 18 altogether with an ankle injury.
Hosts AFC Wimbledon made one change, with Joe Pigott on the bench and Paul Robinson returned to the XI.
Just two minutes in and a high cross from the right was headed away by Jack Payne and fell to Jon Meades, who fired comfortably wide of Raya's goal.
Raya was called into action to head clear a high and pacy ball forward from home goalkeeper George Long, and thankfully, the Spaniard got there just before striker Lyle Taylor.
For Rovers, Darragh Lenihan fired wildly over Long's upright after a neat spell of patient play from the visitors midway through the half.
It wasn't the most fluid of opening periods from the visitors, but it was Rovers who did take the lead in fortuitous or ingenius circumstances through the returning Dack.
A deep Payne cross found his fellow playmaker at the back post, and from the byline, Dack looped a header over Long and over the line to hand his side the lead on the half hour mark.
Rovers were looking for a second goal and seven minutes later Charlie Mulgrew went close from a direct free kick, which took the slightest of deflections and went the wrong side of the post.
Payne was next to try his luck moments later but saw his powerful, low effort held by Long and Rovers went into the break with the narrow advantage.
After the break, the hosts made a change with Pigott replacing Andy Barcham, and the next goal was going to be key.
Danny Graham fired into the side-netting after being fed by Derrick Williams down the left side.
Wimbledon weren't out of it and Rovers were fortunate that after seeing his first shot blocked, Taylor scooped his follow up over Raya's upright.
There was a lack of chances from both sides but just after the hour the visitors grabbed their second of the night, coming through the right boot of Bennett.
After some neat play, the ball found the midfielder, who took a touch before curling superbly into the bottom corner of the net from 25 yards.
Just five minutes later and Rovers had a third, with Dack grabbing it in delightful fashion.
A low cross from the left from Graham was inch-perfect for partner in crime Dack, who brilliantly dinked a first time touch with the outside of his boot over Long and into the back of the net, which was met by great celebrations in the away end and applause from the home supporters, too.
It was a sensational five minutes from Rovers, who really killed off any chance of a home comeback, and Mowbray even had the luxury of handing Graham a rest for the final 15 minutes, with Joe Nuttall replacing the experienced frontman.
Dack's classy second ensured Rovers would see out the final part of the game in comfortable fashion and now the focus turns to Sunday's clash against Wigan at Ewood Park.
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AFC Wimbledon: Long, Fuller (c), Meades, Oshilaja, Robinson, Francomb, Abdou, Forrester, Trotter (Soares, 78), Barcham (Pigott, 46), Taylor (Parrett, 78).
Unused substitutes: McDonnell, McDonald, Kaja, Kennedy.
Rovers: Raya, Nyambe, Lenihan, Mulgrew (c), Williams, Bennett, Smallwood, Payne (Evans, 59), Dack, Armstrong (Antonsson, 80), Graham (Nuttall, 75).
Unused substitutes: Leutwiler, Caddis, Bell, Downing.
Goals: Dack, 31, 69, Bennett, 64,
Booked: Nyambe, 7
Attendance: 4,401 (778 away).