In what was a game of few chances, it took until the dying seconds of the game for a winner to be decided.
Healey, who had re-joined the Club earlier in the summer, found the back of the net with seconds remaining.
Naming his first team of the Sky Bet League One campaign, Paul Tisdale handed full debuts to summer arrivals Hiram Boateng and Jordan Bowery.
The rest of the starting XI was familiar to the MK Dons fans, with Lee Nicholls starting between the sticks with Callum Brittain, George Williams, Russell Martin, Joe Walsh and Dean Lewington ahead of him.
In midfield, Boateng sat alongside Jordan Houghton and Conor McGrandles, while Kieran Agard and Bowery led the line.
In what was a nervy start for both sides, it took until the fifth minute for the first shot of the game as Bowery looked to open his account in spectacular fashion.
Having received the ball in the air from Williams, Bowery took one touch to flick over his shoulder before volleying just over O’Leary’s bar.
George Williams then found himself with space on the right and having set himself, picked out the run of Agard. Shrewsbury’s Ro-Shaun Williams was there to head behind, however, he would injure himself in the process - he was replaced by Omar Beckles.
The Dons would go close from the following corner, but Shrewsbury defended in their numbers before McGrandles’ effort ended over the bar.
Steve Morison, who was leading the line for Shrewsbury Town, looked a danger up front. His clever movement inside the box created some space, his delicate chipped effort hit the side netting.
Lewington then put in a dangerous low cross into the corridor of uncertainty, a delivery that was met by Bowery. His glancing header was well watched by O’Leary who claimed at the front-post.
Shrewsbury Town almost took the lead, but for a crucial interception from Joe Walsh. It came from the wide left as Giles’ cross looked to have picked out McCormick, just as it looks as if the Shrewsbury man would put his side ahead, Walsh somehow turned onto the bar before Nicholls claimed to keep the scores level at the break.
The early staged of the second-half were dominated by the away side, however, a number of crosses were headed away by Martin.
With the second-half lacking any real chances, it took until 70-minutes before either keeper was called into action. Boateng found himself with the ball just outside Shrewsbury's box, and after beating two defenders, he opted to cross instead of shoot. His pass was met by the chest of Bowery, but he was unable to generate enough power to trouble O'Leary.
Shrewsbury then had the chance to open the scoring on the counter. O'Leary claimed Lewington's corner before setting his free, however, the final ball into the box was met by Nicholls who read the situation well.
With the game entering the final five minutes, the Dons had penalty appeals turned away after Joe Walsh was pushed inside the box, Brett Huxtable, however, waved away the appeals.
Nicholls then produced the save of the match as he tipped Dave Edwards' dipping volley behind for a corner before Tisdale's side stood firm from three set-pieces.
With the game drawing to a close, Healey popped up with a late winner and sent the Stadium MK crowd into a rapturous cheer.
MK Dons Starting XI:
Nicholls, Williams, Lewington, Walsh, Bowery (Agard 72,) Agard, Martin (Cargill 78) McGrandles (Reeves 72,) Houghton, Brittain, Boateng.