A solitary strike from Peter Etebo earned all three points for Stoke City at a sun-drenched Ewood Park.
Etebo lashed home from the edge of the box early on in East Lancashire, giving David Raya no chance with a powerful strike.
And that proved the ultimately be the difference, with Rovers finding life tough against a resolute Stoke backline, who kept a fifth consecutive clean sheet with the result.
Rovers were thankful to Raya for keeping the result as it was, with the Spaniard saving a penalty on the stroke of half time before producing a wonder save to stop Sam Vokes from adding to Stoke's tally in the second 45 minutes.
Adam Armstrong probably had the best opportunity for Rovers, but his drive was beaten away by England international goalkeeper Jack Butland just after the break.
Tony Mowbray made three changes to his starting lineup, with Corry Evans and Richie Smallwood coming in for Lewis Travis and Craig Conway, whilst Joe Rothwell earned a start in place of Bradley Dack.
Evans returned from injury, which kept him out of last weekend's game at Aston Villa, whilst Smallwood started after being an unused substitute in the last three outings.
Rovers started brightly, with the returning Rothwell testing Butland after only two minutes, before Armstrong clattered the crossbar five minutes later after wriggling away from the experienced Ryan Shawcross in the Stoke box.
At the other end, Darragh Lenihan was in the right place at the right time to stop Etebo from opening the scoring, but there was nothing he could do to stop the Nigerian a moment later.
Tom Ince was involved again down the Stoke right, with his neat pass being crashed home from the edge of the box by Etebo to hand the visitors the lead after 14 minutes.
Rothwell was growing into the game and lashed wide of target before the half hour mark as Rovers went in search of a quick-fire equaliser against a Potters side who had kept four consecutive clean sheets coming into the clash.
The visitors had a chance to make it 2-0 on the stroke of half time from the penalty spot after skipper Charlie Mulgrew slid in and took down Benik Afobe.
Former Barcelona man Bojan stepped up, but saw countryman Raya in his way, with the Spaniard pushing away the ex-AC Milan playmaker's placed attempt.
The interval probably came at a good time for the hosts, who had to replace Mulgrew due to injury, with Derrick Williams coming on in place of the Scotland international.
There was a change in the visiting ranks early into the second half, with Ashley Williams replacing Stoke skipper Ryan Shawcross, who limped off through injury.
Rovers were improving, and a driven effort from Armstrong stung the palms of Butland, with Raya's earlier penalty save seemingly boosting Tony Mowbray's men.
Stand-in skipper Elliott Bennett was next to try his luck, but after being fed by Rothwell, the 30-year-old fired just wide of Butland's right-hand post.
Time was running out for Rovers to earn a point, and with seven minutes remaining Raya produced a save of the season contender to deny former Burnley man Sam Vokes.
A pinpoint cross from the right found the burly frontman, whose downward header was set to nestle into the bottom corner before Raya sprang to flick away the effort to keep Rovers in the encounter.
Rovers threw caution to the wind late on, but the visitors held on to the three points and Mowbray's men were left frustrated once again.
Rovers: Raya, Nyambe (Brereton, 77), Lenihan, Mulgrew (c) (D. Williams, 46), Bell, Smallwood (Travis, 73), Evans, Bennett, Rothwell, Armstrong, Graham.
Unused substitutes: Leutwiler, Reed, Rodwell, Conway.
Booked: D. Williams, 75
Stoke City: Butland, Allen, Ince (Clucas, 39), Etebo, Afobe, McClean, Batth, Martins Indi, Shawcross (c) (A. Williams, 52), Bojan (Vokes, 60), Edwards.
Unused substitutes: Federici, Vokes, Adam, Clucas, Verlinden, Woods.
Goal: Etebo, 14
Referee: Geoff Eltringham.
Attendance: 17,478 (1,989 away)