Former Dons striker Izale McLeod wasted a glorious chance to open the scoring in only the third minute when he mis-kicked with the goal at his mercy after being set up by Gavin Tomlin.
But McLeod put Crawley ahead from the penalty spot in the 14th minute with his 10th goal of the season.
The striker, who missed a spot-kick against the Dons in August, coolly sent goalkeeper Dave Martin the wrong way after being tripped by former Crawley defender Kyle McFadzean.
Crawley’s Danish goalkeeper Brian Jensen was forced off injured six minutes before the break when dislocating a finger while diving at the feet of the on-rushing Samir Carruthers.
With no goalkeeper included in their five-man bench, veteran striker Matt Harrold took over between the posts.
McLeod cashed in on poor defending to double Crawley’s lead three minutes after the break with a low shot from the edge of the area.
There was a moment of controversy when Dons midfielder Carl Baker ran off the field and jabbed a finger towards a spectator, but referee Graham Salisbury took no action after speaking to Baker and a steward.
Stand-in goalkeeper Harrold, with Jensen standing behind the goal to encourage him, produced saves to deny Ben Reeves and Alli.
Harrold was beaten in the 76th minute when Grigg looped in a header from an assist by Reeves and Alli grabbed a point for the Dons by scrambling home an equaliser deep into stoppage time.