Grigg's superb solo effort after 18 minutes proved decisive for the battling Saddlers, who had already ensured survival last week and left the Dons facing the second leg of their play-off away to Huddersfield.
Walsall had the better of a low-key first half and Emanuel Ledesma twice went close early on, firing straight at goalkeeper David Martin before drilling another shot into the side-netting.
Grigg deservedly put the Saddlers ahead when he skinned defender Tom Flanagan in the box and curled a fine finish inside the far post past. Walsall winger Alex Nicholls then drilled an angled shot narrowly wide before Ledesma again fired straight at Martin when clean through.
The Dons came out with more purpose after the break but they were restricted to shots from distance. And Jamie Paterson should have doubled Walsall's lead from a swift late counter-attack but he curled the ball wide when one-on-one with Martin.
The Dons played the last 13 minutes with 10 men after substitute Luke Chadwick limped off injured, and Saddlers defender Manny Smith had a last-gasp header cleared off the goalline line by Flanagan.