Rory Fallon gave the rock-bottom Robins a half-time lead, but goals from Malvin Kamara, Gareth Edds and Izale McLeod ensured the Dons' revival continued as Swindon slumped to their seventh successive defeat.
Wilson named the same team that beat Scunthorpe 1-0 on Tuesday, with Edds and Kamara continuing to deputise for the injured Trent McClenahan and Wade Small.
Milton Keynes started brightly and McLeod wasted a golden opportunity to put them ahead in the third minute when he raced onto Clive Platt's lofted through ball but fired straight at goalkeeper Tom Heaton.
But Swindon hit back and after Colin Heath's 35-yarder was tipped over the bar, he curled in the resulting corner for Fallon to break the deadlock in the seventh minute.
Heath's out-swinging corner found Fallon unmarked at the near post and he dived to head home his sixth goal of the season.
At the other end, Edds stung Heaton's fingers with a rasping 30-yard free-kick that the keeper tipped over the bar before McLeod smashed a 25-yard drive just over the bar as the Dons battled for an equaliser.
Edds forced Heaton into a decent low save with another long range free-kick before McLeod rode Swindon skipper Sean O'Hanlon's tackle and smashed in a fierce angled drive that the Swindon keeper acrobatically tipped over the bar.
But Milton Keynes were not to be denied and Kamara equalised just four minutes after the re-start with his first goal of the season.
Paul Mitchell chipped it forward and Kamara snuck it between O'Hanlon and Jack Smith to race away and slot home from 12 yards with the outside of his right boot.
Swindon should have regained the lead in the 63rd minute when the unmarked Fallon and then O'Hanlon slid in on Heath's in-swinging corner but both somehow failed to touch it in from close range.
At the other end, Stephen Quinn's perfectly weighted through ball set McLeod away in the 68th minute but again the striker's finishing was wayward as he sliced it wide.
But Dons went ahead nine minutes later thanks to Edds' close-range finish. Substitute Nick McKoy's cross was spilled by Heaton and after Quinn flicked it across goal Edds was there to poke it home from close range.
The home side then piled on the pressure and after Edds had an effort cleared off the line by Swindon full-back Smith and substitute Aaron Wilbraham had struck the bar from 25 yards, McLeod sealed the win in the 81st minute.
Dean Lewington's cross was flicked on by Wilbraham at the near post and McLeod bagged his fourth goal of the season with a close-range diving header.