Matt Tubbs made it three goals in three starts for AFC - but his winner notched Dons their first three points of the campaign.
His strike four minutes before the break when Ade Akinfenwa flicked on for Tubbs to take a touch and fire past Hatters keeper Mark Tyler.
Akinfenwa might have doubled the score shortly after half-time, but he nodded George Francomb's free-kick against the post from close rage.
A change at the back brought in Adam Barratt, whose early header cleared the bar.
In the closing stages, Luke Guttridge went close for Luton with a header for Luton, while Mark Cullen hit the post with a low shot.
And although it was disappointing for most of the 9,000 packed crowd inside Kenilworth Road on Luton's return to the League, the 690 travellers in blue-and-yellow were delighted with the win that shoots Dons up to seventh with four points from six.
Dons: AFC Wimbledon: James Shea, Barry Fuller, Dannie Bulman, Alan Bennett, George Francomb (Kevin Sainte-Luce), Sammy Moore, Matt Tubbs (Ade Azeez), Bayo Akinfenwa, Sean Rigg (Harry Pell), Callum Kennedy, Adam Barrett.