© Getty Images
The Gunners, searching for a first opening-day win since 2009, went behind on 35 minutes courtesy of Brede Hangeland's goal.
However, Arsene Wenger's side responded well and restored parity in timely fashion through Koscielny's firm header moments before the half-time whistle.
Tony Pulis's resignation dominated the build-up to the encounter, but the Eagles produced a disciplined first-half performance under Keith Millen and made the Gunners work hard for an opening.
The hosts struggled to build on that opportunity and Millen's side went ahead with 10 minutes remaining in the half, as Hangeland rose highest to plant a header past Wojciech Szczesny.