Karl Robinson’s side cut open the Railwaymen with ease in a one-sided first half and Cole, on loan from Manchester City, scored twice as the Dons swept home three goals.
The 19-year-old opened the scoring in the 12th-minute, finishing off the rebound after a Dean Bowditch shot was pushed out by goalkeeper Ben Garratt.
Bowditch drifted all too easily behind the home defence to bring down Darren Potter’s lofted pass and chip Garratt for the second in the 27th minute.
And eleven minutes later, Cole was offered an easy finish after Daniel Powell cut the ball back from the right with Crewe’s defence at full stretch again.
Jamie Ness went close for the hosts with a free-kick and substitute Anthony Stewart’s header needed a save from Dons keeper David Martin.
But Robinson’s men toyed with the Alex at times in the second half and Carl Baker added a fourth goal when he cut in from the left to shoot into the far corner of the net after 72 minutes, before then clipping the crossbar with an exquisite chip.
Powell completed the rout when he drove a low shot into the bottom corner in the last minute.