Rovers' play-off hopes were dealt a blow on home turf as table-topping Leeds United returned back across the Lancashire-Yorkshire border with all three points
An error from Lewis Travis early on allowed Kalvin Phillips to feed Patrick Bamford, who made no mistake after only eight minutes of play at a drizzly Ewood Park.
Rovers missed good chances through Sam Gallagher and Lewis Holtby, before Phillips' superb free kick doubled the visitors' advantage just before half time.
Adam Armstrong brilliantly struck home his own super free kick to give the hosts hope of a comeback, but Mateusz Klich made the points safe for Leeds soon after.
The result ensured Leeds kept their spot at the top of the table, whilst Rovers have plenty of work to do if they are to finish in the top six.
Tony Mowbray made three changes to his starting XI, with Darragh Lenihan, Travis and Gallagher all returning in place of Charlie Mulgrew, Stewart Downing and Dominic Samuel.
For the visitors, Marcelo Bielsa opted for two alterations, with Barry Douglas and Gjanni Alioski coming in for the injured Stuart Dallas and Helder Costa.
It was ex-Leeds man Bradley Johnson who had the first shot in anger, but his effort from the edge of the box was well held by young French goalkeeper Illan Meslier after only three minutes played.
However, with the visitors' first opportunity came the first goal. The returning Travis was caught in possession by Kalvin Phillips, and the midfielder's simple pass fed Bamford who slotted home for his 15th goal of the season.
Rovers looked for a quickfire equaliser, and it nearly arrived through the right foot of Gallagher, but he fired wide when one-on-one with Meslier.
A moment later and Rovers went closer to working a leveller, but Lewis Holtby crashed an effort against the post after Gallagher fed the German midfielder.
The half hadn't even got to the mid-point before Rovers had to make their first change, with Downing coming on for the injured Elliott Bennett and slotting into the left back position.
A Rovers post was hit just before the half hour mark, with Bamford's effort hitting the base of Walton's right-hand post after Luke Ayling's strike was blocked and fell kindly into his team-mate's path.
A fine corner kick from Douglas almost caught Christian Walton out, with only the fine reactions from the Brighton & Hove Albion loanee denying the Scot.
But Leeds didn't have to wait too much longer to double their lead, and they added to it in style thanks to star man Phillips.
The midfielder bent a free kick from 25 yards into the top corner, giving Walton no chance with just four minutes to go until the break.
The goal knocked the wind out out of Rovers' sails going into the interval, but what happened just after the restart ignited life back into Mowbray's men.
That's because Armstrong delivered another blockbuster of a goal to add to his portfolio just three minutes into the second half.
It was the diminutive frontman who earned the free kick after being taken down on the edge of the box by Phillips, and delivered a peach of a set piece that gave Meslier no chance.
However, Leeds restored their two-goal advantage just five minutes later through Mateusz Klich. Rovers didn't clear their lines well enough and the Polish midfielder volleyed into the bottom corner from just inside the box.
There were just over 15 minutes remaining until the net opportunity arrived for either side, with Douglas' free kick being well saved by Walton after the Rovers 'keeper brought down Bamford on the edge of the box when the Leeds man was clean through.
At the other end, substitute Samuel tried his luck from range, but his effort was comfortable for French stopper Meslier to hold.
United managed to see the game out comfortably enough to secure a valuable win, whilst Rovers will hope for better fortunes when they head to Cardiff City on Tuesday night, kick-off 7.45pm.
Rovers: Walton, Nyambe, Lenihan, Adarabioyo, Bennett (c) (Downing, 22), Rothwell (Buckley, 69), Travis (Davenport, 69), Johnson, Gallagher (Graham, 60), Holtby (Samuel, 60), Armstrong.
Unused substitutes: Leutwiler, Chapman, Mulgrew, Carter.
Goal: Armstrong, 48
Booked: Walton, 74
Leeds United: Meslier, Ayling, Douglas, White, Cooper (c), Bamford, Alioski, Roberts (Hernandez, 61), Harrison, Phillips, Klich (Shackleton, 89).
Unused substitutes: Miazek, Poveda, Berardi, Struijk, Gotts, Davis, Stevens.
Goals: Bamford, 8, Phillips, 41, Klich, 53
Booked: Klich, 26, Ayling, 29.
Referee: Robert Jones.