Bradley Johnson, on loan from Leeds, gave the Seagulls a dream start in only the third minute with a superb finish following a free-kick by Glenn Murray.
But Spaniard Miguel Angel Llera deservedly levelled in the 27th minute by turning in a corner from Jason Puncheon.
Aaron Wilbraham was denied by the post before the break, but Jemal Johnson drove Dons ahead just a minute after the restart.
Scotsman Peter Leven made the game safe with 20 minutes remaining by pouncing on slack defensive play by Tommy Elphick to slot home from six yards.
Substitute Stuart Fleetwood struck from long range with two minutes remaining to give Brighton hope, but Puncheon's superb 89th-minute solo effort sealed the Dons' sixth win in their last seven away league games.