Grigg's brace plus goals from Febian Brandy and Jamie Paterson handed the Saddlers a second successive win, while Ryan Lowe and Dean Bowditch were both on target for the below-par Dons.
Lowe put the Dons ahead after only six minutes when he stole in unmarked to head home Adam Chicksen's cross for his fourth goal in as many games.
But Walsall scored two goals in 10 minutes to turn the match on its head, first when Brandy bundled his way through to lash the ball into the top corner and then when Grigg skinned Mathias Doumbe to curl the ball past David Martin.
Dons forward Bowditch made it 2-2 when he neatly slotted in Lowe's lay-off, but Grigg restored Walsall's lead two minutes before the break, tapping in Craig Westcarr's low cross from close range.
The Dons struck the woodwork twice after the break as substitute Patrick Bamford had a shot deflected against the post and Antony Kay headed against an upright,
But after Grigg had also been denied a hat-trick by the woodwork as his header hit the crossbar, Paterson made it 4-2 in the 90th minute when his curling shot was deflected past Martin.