Powell's 27th-minute tap-in ended the Seagulls' three-match winning run as the Dons survived a late onslaught after Sean O'Hanlon's 67th-minute red card.
Dons winger Keanu Marsh-Brown was twice denied by keeper Casper Ankergren early on, first when his low shot was well saved after a mazy run and then when his fierce half-volley was acrobatically tipped over the bar.
But Powell deservedly put the Dons ahead just before the half-hour mark, slotting home the rebound from close range after O'Hanlon's header had come back off a post.
Powell drilled another effort narrowly wide soon after the break and Rowan Vine had a strong penalty appeal waved away after going down under a challenge from Marcos Painter.
Ankergren then superbly saved Stephen Gleeson's drive before Brighton striker Chris Wood was denied by a brilliant double save from Dons keeper David Martin, who saved his close-range header and then his follow-up attempt. O'Hanlon received his second booking for a late tackle on Glenn Murray near the halfway line but the Dons hung on for their first win in five games at stadium:mk.