The Dons were cruising to victory with just 15 minutes remaining as first-half goals from Aaron Wilbraham and Jason Puncheon put Roberto Di Matteo’s men in control.
But two goals in the space of three minutes drew Alex level – Mark Carrington heading home before Sigurdsson converted a spot-kick after keeper Willy Gueret had felled Alan Sheehan.
The Dons were soon in front as Wilbraham’s effort struck defender Marlon Broomes and looped over a stranded keeper John Ruddy after 15 minutes. Puncheon then doubled the lead in the 19th minute when his weak effort slipped through Ruddy’s hands.
Crewe’s attacks were few and far between but Sigurdsson did sting the palms of Gueret on the stroke of half-time before Sam Baldock hit the post from close range for the Dons.
But there was late drama as Carrington grabbed one back for Crewe with a 77th minute header before Sigurdsson hit the leveller from the spot three minutes later to snatch a draw.