Arsenal 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 Jake 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 weren't creating anything of note as the visitors' defence held strong.
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 his move, with Jack Wilshere, Theo Walcott and Santi 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 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, Blackburn held on to progress to the quarter-finals.