The tricky winger, who helped Kenny Jackett's side to a 7-1 win over Bristol City on Saturday, grabbed two goals in the last 18 minutes after Pablo Mills had equalised Lee Trundle's opener for the visitors.
Dons' boss Wilson sprang a shock in his starting line-up, naming Izale McLeod up front after his speedy recovery from a dislocated shoulder.
Aaron Wilbraham dropped to the bench to make way for the top scorer, while Dean Lewington recovered from a dead leg to replace Mirano Carrilho and Malvin Kamara replaced the injured Wade Small (hamstring).
But it was Swansea who had the better of the early exchanges and Robinson twice came close to breaking the deadlock in the first 12 minutes.
First he whipped a 20-yard free-kick just over the bar in the 11th minute with goalkeeper Matt Baker stranded.
And then a minute later the tricky winger blasted a fierce effort just wide from 10 yards after a good run from Trundle.
But the Swans didn't have to wait long to take the lead as Trundle latched on to skipper Roberto Martinez's through ball before coolly slotting past Baker in 16th minute while the defence appealed for offside.
The Welshmen continued to pile on the pressure and Baker produced a fantastic save to turn Paul Connor's close-range glancing header round the post from Robinson's cross.
But Milton Keynes got a rare chance to attack when a poor defensive header gave them their first corner of the match in the 35th minute. And they made it count as Mills equalised with a powerful header from Lewington's kick.
McLeod was then denied by Willy Gueret from just seven yards as the Dons fought their way back into the match, before his Swansea namesake Kevin McLeod blasted a good chance over the bar at the other end.
The Dons improved after the break and Kamara was twice unlucky not to give them the lead.
First he raced onto Lewington's quick free-kick and fired in a fierce angled drive that Gueret blocked well and then his volley from substitute Nicky Rizzo's cross dropped inches wide.
But Swansea hit back and the superb Robinson put the game beyond the Dons with two quick goals in six minutes.
He latched on to Trundle's through ball and rounded Baker to put them back in front in the 72nd minute before making it 3-1 with a fierce strike across the keeper 13 minutes from the end.