The hosts were short on creativity, particularly in the first half, and they bypassed another chance to end their trophy drought after crashing out of the FA Cup.
Arsene Wenger's side dominated much of the game but found chances difficult to come by, particularly in the first half, and found goalkeeper Jake Kean and the crossbar blocking their route to the quarterfinals.
Wenger selected a strong team for their tie against Rovers, with Thomas Vermaelen starting despite being the only player available to start at left back against Bayern Munich in the Champions League on Tuesday.
Elsewhere, Olivier Giroud and Gervinho were in attack, while there was also a strong presence on the bench, featuring the likes of Theo Walcott, Jack Wilshere, Santi Cazorla and Lukas Podolski.
For Blackburn, there was a place on the bench for former Gunner David Bentley, who famously scored from nearly 40 yards against Arsenal for parent club Tottenham in a remarkable 4-4 draw.
Wenger's side had plenty of the ball in the opening stages, but despite a succession of corners, the Gunners 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 67th minute heralded the first real moment of note in the second half, 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.
With 20 minutes to go, Wenger made a triple substitution, with Wilshere, Walcott and Cazorla replacing Gervinho, Rosicky and Alex Oxlade-Chamberlain.
But it didn't 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 Wojciech Szczesny, but only back in front of goal, and Kazim-Richards was on hand to bounce an awkward shot home off the post.
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 an effort into the side netting as Wenger's side crashed out of the FA Cup.