Brentford dominated large parts of the game but strikes from Bowditch and Gleeson either side of the interval secured a second successive win for the Dons, ending the Bees' three-match winning streak.
Bowditch put the Dons ahead against the run of play in the 14th minute when his speculative 25-yard shot squirmed underneath goalkeeper Simon Moore and into the corner of the net.
Forward Harry Forrester had two fierce strikes saved by Dons keeper Ian McLoughlin, who also beat out a close-range header from skipper Jonathan Douglas.
Marcello Trotta then missed a golden opportunity to equalise when he fired wide one-on-one with McLoughlin before Patrick Bamford drilled a low shot against the post for the Dons on the stroke of half-time.
The Bees bossed the second half and substitute Bradley Wright-Phillips flashed a header just over the crossbar, while Toumani Diagouraga and Harlee Dean were both narrowly off-target.
But Gleeson sealed a smash-and-grab win for the Dons five minutes from the end when he lashed in Darren Potter's cutback.