Blackburn started impressively against their Premier League opponents but neither side enjoyed a spell of sustained pressure early on at the Emirates Stadium.
The Gunners started to take control of the contest midway through the first half and Jake Kean had to be alert to keep out Abou Diaby's header with a fantastic save.
Arsenal continued to dominate until the interval but a lack of composure in the final third of the pitch meant that the two sides headed into the break on level terms.
Michael Appleton's team carried their work ethic into the second half, frustrating the Arsenal forwards with some stubborn defending.
Tomas Rosicky was inches away from opening the scoring but his powerful effort struck the crossbar, with Kean looking helpless in goal.
Despite sending on Jack Wilshere, Theo Walcott and Santi Cazorla just after the hour mark, Arsene Wenger saw his side fall behind when Kazim-Richards converted from close range after Wojciech Szczesny had denied Martin Olsson.
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