The hosts were short on creativity against the Championship outfit, and could now go eight years without a trophy should they fail to lift the Champions League this term
Arsene Wenger's side dominated much of the game, but found chances difficult to come by, with opposition goalkeeper Jake Kean and the crossbar conspiring to block their route to the quarter-finals.
Wenger selected a strong starting line-up for the game, with Thomas Vermaelen picked despite being the only player available to start at left-back against Bayern Munich on Tuesday.
ARSENAL 0-1 BLACKBURN
For Blackburn, there was a place on the bench for former Gunner David Bentley, who famously scored from near-40 yards against Arsenal for parent-club Tottenham in a remarkable 4-4 draw in 2008.
Wenger's side had plenty of the ball in the opening stages, but despite a succession of corners, could not create any clear opportunities until the 24th minute, when Abou Diaby forced a good save from 22-year-old goalkeeper Kean with a header.
Kean was called into action again minutes later, when a deflected defensive header looped towards his goal, but the keeper clawed it out for yet another corner.
With the first half drawing to a close, the clearest opening of the match came and went as Gervinho was threaded through by Tomas Rosicky, only to place his shot wide of Kean's post, having sent the keeper the other way.
The first 45 minutes drew to a close with the sides level, and the game in need of something to ignite it in the second half.
There was early pressure from the Gunners in the second half, but they still were not creating anything of note as the visitors' defence held strong - a theme that continued into the last quarter of the match.
The 67th minute heralded the first real moment of note in the second period, as Rosicky struck a stunning effort from 25 yards that crashed back off Kean's crossbar, while Gervinho was sent through on goal only to be denied by a last-ditch tackle from Grant Hanley.
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But it did not have the desired effect as just one minute later, the Gunners were split open by a long ball. Martin Olsson's strike was pushed out by Szczesny, but only back in front of goal, and Kazim-Richards was on hand to bounce an awkward shot home via the post.
The stage was set for a Gunners onslaught, and they duly obliged with the visitors dropping deeper and deeper in a bid to protect their lead.
But, despite their dominance, the chances were not being converted. Monreal dragged two shots wide, Walcott had a penalty appeal turned down after being incorrectly adjudged offside, and Diaby had an effort pushed away by Kean with five minutes to go.
With two minutes to go, the Gunners spurned another chance as Walcott headed an effort straight at Kean, while an injury time shot from Giroud was cleared off the line and Arteta smashed into the side netting as Wenger's side crashed out of the FA Cup.