Philippe Senderos headed home Eduardo's corner to give Arsenal an early lead. But Rovers quickly dug in and the Gunners did not threaten again until Alex Hleb hit the post after the break.
Blackburn keeper Brad Friedel denied Emmanuel Adebayor twice but the Togo striker added a late second when he drilled his shot home in injury time.
Sunday's results - which saw second-placed Manchester United lose to neighbours Manchester City and third-placed Chelsea held by Liverpool - had handed Arsenal the advantage in the title race.