A point for Arsenal would have guaranteed third and an automatic place in next season's Champions League group stage but after Robin van Persie put them ahead they were overhauled by a fired-up Rovers.
"It could have gone both ways, but overall Blackburn were sharper in the duels and in the fights than us," Arsenal manager Arsene Wenger said. "Then it becomes very difficult to win football games."
Arsenal have 72 points with just Fulham to play at home on Sunday while fourth-placed Tottenham Hotspur have 67 with Wednesday's crucial trip to direct rivals Manchester City and a final day visit to relegated Burnley to come.
"I believe we do not have to worry about Tottenham or Manchester City. We have to worry about us and finish well this season," Wenger added.
At the other end of the table Hull City's relegation was rubber-stamped when Wigan Athletic equalised in stoppage time to deny the visitors their first away league win of the season.
The 2-2 draw, courtesy of an equaliser by Steve Gohouri, means Hull are five points behind 17th-placed West Ham United with one game to play, though even a win would have been futile as their vastly inferior goal difference would have counted against them even if they had matched the London club on points.
Hull will go down to the Championship next season along with Burnley and Portsmouth, having lasted two years in the top flight.
Since beating West Ham on March 20, Arsenal have managed just a stoppage time victory over Wolverhampton Wanderers in their subsequent eight matches as their Premier League and Champions League hopes evaporated.
Finishing outside the top three would have been unthinkable a few weeks ago when Arsenal still harboured genuine hopes of ending their five-year wait for a trophy but they could face a jittery final day at home to Europa League finalists Fulham.
Van Persie gave Arsenal an early lead, heading in a corner.
Rovers levelled through David Dunn's tap-in shortly before half time and Chris Samba beat Lukasz Fabianski with another header midway through the second half to seal victory for mid-table Rovers.
Wenger, never a big fan of Blackburn's robust style of football, criticised the referee for both the goals and said Fabianski should have been protected.
"You have no chance as a keeper to go for the ball if every time you go somebody pushes you," Wenger said.
"The two players in front of him every time had only one purpose - to stop him from getting the ball. That does not take away from the fact that we were not good, but that's completely unfair for me."
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