It was a frustrating afternoon for visiting boss Arsene Wenger, who appeared to be unhappy with what he saw as Rovers' robust approach to the contest.
On the field, Fabianski repeatedly complained to referee Martin Atkinson, although replays suggested that on several occasions at least, Rovers were guilty of nothing more than standing their ground.
Arsenal had settled quickly and Theo Walcott's blistering pace created a fourth-minute opening that Carlos Vela, making his first Premier League start since the closing stages of last season, should have converted but missed from six yards.
Rovers were the next to threaten, with Fabianski diving sharply to his right to save a free-kick from Pedersen, but Arsenal clearly possessed the greater cutting edge in the early stages and took the lead after 13 minutes.
Bacary Sagna flicked on a corner at the near post and Van Persie headed home unmarked to score his 10th goal in nine games against Rovers.
Paul Robinson parried a free-kick from Van Persie, while Pedersen again forced Fabianski into action with a dead-ball strike that swerved viciously.
Rovers took every opportunity to test the handling of Fabianski, who landed heavily on his right knee as he jumped above Sol Campbell to collect a loose ball.
Wenger cannot understand ref decisions
The Arsenal keeper was able to continue but he was picking the ball out of his net shortly before the break after his team failed to deal with a corner.
The ball eventually fell to Keith Andrews, who drilled a low cross back across goal that several Arsenal players failed to clear, gifting Dunn a simple tap-in.
It had been an entertaining opening half in the spring sunshine at Ewood Park - and the openings continued after the break.
Andrews played an excellent through ball to Pedersen, whose shot was parried by Fabianski. Pedersen chased the rebound and went down under a challenge from Campbell but Atkinson was not interested in his penalty appeals.
Dunn played Hoilett through, with the substitute forcing Fabianski to tip his strike over the crossbar, before Arsenal threatened to regain the lead.
Van Persie embarrassed Michael Salgado with a sharp turn but the Dutch striker lost his footing as his opponent tried to rescue the situation. Once again, Atkinson waved away the penalty appeal.
Mikael Silvestre almost diverted a flick-on into this own net as he tried to clear the danger, but Rovers scored the winner after the visiting team failed to deal with the physical presence of Samba.
Allardyce targeted 'weak Arsenal defence'
The Rovers skipper stood close to the Arsenal goal-line as a corner was delivered and finished the simplest of headers after both Fabianski and Campbell failed to clear the danger.
Arsenal substitute Andrey Arshavin forced a decent save from Robinson but Rovers held out to ensure that they avoided defeat against the Gunners, Manchester United, Chelsea and Liverpool at home this season.
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