Two first-half goals from Alan Bennett and Matthew Tubbs seemed to have given the Dons a memorable victory over their Premier League opponents, but Jose Mourinho's men scored three times in the final quarter of an hour to ensure that they weren't embarrassed by the League Two side.
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Bennett rose highest from a corner and planted a header inside Mark Schwarzer's near post to give the home side the lead just 38 seconds after kickoff, while Sean Rigg and George Francomb also went close for the hosts in the opening period.
Shortly before the break, Kurt Zouma bundled over Tubbs, who stepped up to strike a confident penalty into the corner to make it 2-0, much to the delight of the home crowd.
After the break, Chelsea looked like a side who had been told in no uncertain terms that their first-half performance wasn't good enough, and Nathan Baker forced James Shea into a good save in the 49th minute.
Two minutes later, Isaiah Brown should have tested Shea again, but the youngster couldn't keep his header down at the far post.
Marco van Ginkel did manage to get an effort on target a few minutes later, but Shea was equal to the header once more.
With little more than 15 minutes left to play, Terry reacted quickly and halved the deficit after Baker's corner had dropped loose in the box.
Salah then levelled the scores with a precise finish after good work from Baker, and the Chelsea skipper Terry glanced a header beyond Shea in the 90th minute to complete a remarkable turnaround.