Arsenal had fought back from behind to lead through a quick-fire pair of goals from Lukas Podolski and Kieran Gibbs in the last 10 minutes, only for Graham to pounce at the death to take a gripping tie to a replay.
Swansea had led through a 58th-minute effort by Michu but appeared to be heading out until Graham found the roof of the net with three minutes to play. Michu began on the bench for Swansea, with an eye on the League Cup semi-final against Chelsea, while Arsenal made three changes and deployed Olivier Giroud as a lone striker.
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