Chris Hughton's side had dropped out of the top two following Middlesbrough's 1-0 victory over Hull on Friday.
But Hemed's introduction in the 52nd minute quickly paid off as he scored the opening goal four minutes later from the penalty spot before making it 2-0 just after the hour mark.
Milton Keynes did pull a goal back through Anthony Kay and, despite Kyle McFadzean's sending off two minutes later, they could have snatched a dramatic draw only for Carl Baker to miss a stoppage-time penalty.
Brighton's dramatic victory lifted them back into second place, one point clear of Middlesbrough, who have a game in hand, as the race for the Premier League enters the home stretch.
It was a miserable end to a forgettable week for the relegation-threatened Dons, whose midfielder Samir Carruthers was fined two weeks wages and suspended for Saturday's match for his part in an incident at the Cheltenham Festival this week.
A national newspaper appeared to show Carruthers and Shrewsbury striker James Collins, currently on loan at Northampton, urinating into a glass and the latter throwing the contents over a balcony.
Leaders Burnley were denied a seventh straight league win as Danny Batth headed a late equaliser to earn Wolves a 1-1 draw at Turf Moor.
Sean Dyche's Burnley looked set to open up a six-point lead over Brighton when Sam Vokes netted his fourth goal in three games in the second half.
But in stoppage time Batth headed home for just his second goal of the season.
Marcus Olsson's first goal for Derby was enough to secure a 1-0 victory over local rivals Nottingham Forest at the iPro Stadium and keep their promotion challenge on track.
Olsson struck 11 minutes from time, with fifth placed Derby's new football advisor Harry Redknapp watching from the directors' box.
Sheffield Wednesday strengthened their grip on the final play-off spot with a 3-0 win over struggling Charlton at Hillsborough.
Cardiff's play-off hopes suffered a setback as they were held to a 1-1 draw at Reading, while Ipswich also lost ground on the top six after a 1-0 home defeat against in-form Rotherham.
Struggling Fulham halted their losing run with a 1-1 draw at Birmingham.
Former Chelsea starlet Rohan Ince gave Fulham a first half lead with only the second goal of his career, but Michael Morrison rescued a point for Birmingham early in the second half.
Despite Fulham's first point from six games, they are just one point above the relegation area.
Elsewhere, 10-man Blackburn won 1-0 at Brentford and Preston drew 1-1 with QPR.
Huddersfield won 4-1 at Yorkshire rivals Leeds, while Bristol City crushed bottom of the table Bolton 6-0.