A superb solo goal from Harvey Elliott wasn't enough as Teem Pukki's brace sent Norwich City home from Ewood Park with all three points.
After Pukki put the visitors into the lead in the first half, the goal of the game came via Elliott's left foot just before the hour mark.
The Liverpool loanee slalomed in-between a couple of City players before prodding under Michael McGovern for his third goal of the season.
However, Pukki got the slightest of deflections off Emi Buendia's long range strike to ultimately win the game for Daniel Farke's Canaries.
But Rovers did have their chances to earn at least a draw throughout the encounter, most notably when Sam Gallagher hit the bar and when Lewis Holtby's volley forced a scrambling McGovern to beat away the strike.
Despite the strong display, Rovers were made to rue missed opportunities, but have a chance to get back on track when Rotherham United visit Ewood Park on Wednesday night.
Both sides made one change to their starting teams, with Darragh Lenihan returning from suspension to come in for Daniel Ayala, whilst Alex Tettey replaced Marco Stiepermann for the visitors.
Rovers came out of the traps the quickest on home turf, and Sam Gallagher saw his glancing header flicked away by McGovern after only six minutes.
Moments later and Elliott curled just past McGovern's right-hand post as the hosts pressed for an early opener.
It was an open game, with chances coming for Norwich as well, but Thomas Kaminski was well placed to grab Pukki's lofted attempt.
But Pukki didn't have to wait too much longer to get his goal midway through the first half.
Tettey kept a move alive, and his cross was the left was controlled well by the Finland international before he swivelled and lashed into the near corner before Kaminski could react.
The striker went in search of his brace, but dragged wide with his left foot after wriggling away from his man with 10 minutes of the half remaining.
Rovers always looked like they could score, but it was dangerman Pukki who could and should have put City 2-0 up on 38 minutes.
The striker was on the spot to latch onto Max Aarons' pull back, but he clipped the post before the follow up attempt was saved brilliantly by Kaminski and then Josh Martin smashed over.
Rovers will have found themselves frustrated to have gone into the interval a goal down and, much like the first half, and Elliott's deflected cross looped just wide a moment before Sam Gallagher thundered a strike against the crossbar inside the opening couple of minutes of the half.
Another opportunity came just seconds later, with former Norwich man Bradley Johnson heading Joe Rothwell's free kick straight at McGoven and then the Northern Irish goalkeeper flew to his right to beat away Holtby's volley.
You felt the goal was coming and it arrived from the delicate footwork of Elliott, who danced past Jacob Sorensen, beyond Hanley and flicked the ball under McGovern and in with almost an hour gone.
However, Rovers were level for only six minutes, with Emi Buendia's strike taking a deflection of Pukki, wrong-footing Kaminski and flying in to hand the visitors the lead for the second time in the game.
It was a hammer blow for Rovers who attempted to lift the spirits, but Armstrong's strike was held by McGovern before Kaminski kept Rovers alive with a couple of minutes remaining when he kept out substitute Todd Cantwell's snapshot.
Another substitute was denied when Kaminski kept out Marco Stiepermann right at the death, but it counted for little as Norwich returned to Norfolk with all three points and kept their spot at the top of the table.
Rovers: Kaminski, Nyambe, Lenihan (c), Williams, Douglas, Johnson (Davenport, 72), Holtby (Buckley, 72), Rothwell (Downing, 72), Gallagher, Elliott, Armstrong.
Unused substitutes: Pears, Ayala, Chapman, Bell, Carter, Dolan.
Goal: Elliott, 59.
Norwich City: McGovern, Aarons, Zimmermann, Hanley (c), Sorensen, Skipp, Tettey, Vrancic (McLean, 66), Buendia (Stiepermann, 90), Martin (Cantwell, 66), Pukki (Hugill, 89).
Unused substitutes: Barden, Dowell, Omobamidele, Omotoye.
Goals: Pukki, 22, 65
Booked: Pukki, 83
Referee: Dean Whitestone.