Substitute Benni McCarthy's wonder goal delivered a second cup knockout blow to Arsenal in the space of four days.
Baptista missed several chances for Arsenal
Beaten in the Carling Cup final on Sunday, Arsenal exited the FA Cup in a game they really should have won.
The Gunners had two reasonable first-half penalty appeals rejected, while Julio Baptista missed with a header and had a couple of shots saved.
And McCarthy punished Arsenal in the most devastating fashion, breaking in from the wing and arrowing home a shot.
Blackburn manager Mark Hughes had opted to keep McCarthy on the bench for the opening hour and Rovers suffered in the absence of their top scorer.
The home side laboured in attack and had to rely on goalkeeper Brad Friedel's reflexes to keep them in the match, just as he had done in the first meeting between the two sides.
McCarthy initially struggled to adapt to the pace of the game, but with four minutes remaining he broke past Philippe Senderos and beat Manuel Almunia with that wonderous strike to score his 16th goal of the season.
Blackburn's reward is a FA Cup quarter-final tie at home to Manchester City.
In truth Blackburn were fortunate to go in at half-time on level terms as both Jeremie Aliadiere and Fredrik Ljungberg had reasonable penalty appeals turned down.
Aliadiere went to ground after Friedel came out quickly as the Arsenal striker threatened.
Friedel ticked off Aliadiere, suggesting the Frenchman had dived and referee Graham Poll remained unmoved by Arsenal's appeals.
Poll was equally dismissive of an appeal from Ljungberg after the Swede tumbled following Brett Emerton's challenge.
On the sidelines Arsene Wenger was flabbergasted no penalty had been given and television replays showed the Arsenal manager might have good reason to be so.
Arsenal had a couple of chances to score from open play, but each time their finishing was awry.
The unmarked Baptista sent a header over the bar, while Ljungberg was let down by poor control when he was in a menacing position.
Having gone close with that header, Baptista tried his luck with his feet, testing Friedel with a couple of powerful shots, though each time the American was the equal of the Brazilian.
Just before the hour, Morten Gamst Pedersen missed Blackburn's best chance when he blazed wide from a promising position.
This was Arsenal's third FA Cup trip this season to the north west, but having beaten Liverpool and Bolton, this journey proved third time unlucky for Wenger's team.
Blackburn boss Mark Hughes:
"The goal deserved to win any game and I can't wait to see it again. Benni brings world-class quality and he's shown that all through the season.
"What a good decision from the manager to bring him on as an impact player!
"We've got a pretty good record against Manchester City and we'll be looking forward to that and hoping to do well."
Arsenal manager Arsene Wenger:
"We were never under pressure and we had lots of chances to score, but we didn't take them.
"It's difficult to take over the two games. We needed to be ruthless, but we were also bit unlucky over the two matches with decisions.
"With Fredrik Ljungberg in the first half it looked a clear penalty."
Blackburn: Friedel, Emerton, Samba, Nelsen, Warnock (Khizanishvili 46), Bentley, Kerimoglu (Dunn 63), Mokoena, Pedersen, Nonda (McCarthy 63), Derbyshire.
Subs Not Used: Enckelman, Roberts.
Booked: Kerimoglu, Dunn, Derbyshire, McCarthy.
Goals: McCarthy 87.
Arsenal: Almunia, Eboue (Walcott 61), Senderos, Gallas, Traore (Clichy 66), Hleb, Denilson, Silva, Ljungberg, Aliadiere, Julio Baptista.
Subs Not Used: Poom, Gavin Hoyte, Randall.
Booked: Traore, Clichy.
Ref: G Poll (Hertfordshire).