Shaun Williams' penalty had given the Dons a half-time lead but super-sub Maguire curled in two exquisite strikes to win it for the Sky Blues after fellow debutant Chris Dagnall had levelled.
The Dons bossed the first half and Daniel Powell should have opened the scoring in the seventh minute but he fired straight at goalkeeper Joe Murphy one-on-one, while Patrick Bamford missed two good chances.
Williams netted his ninth goal of the season to put the home side ahead on the stroke of half-time, sending Murphy the wrong way from the penalty spot after Dan Seaborne had shoved over Ben Reeves in the box.
But Coventry seized control after the break and Dagnall equalised in the 65th minute when his fierce deflected shot looped up over helpless goalkeeper Ian McLoughlin.
On-loan Sheffield Wednesday forward Maguire then sealed the Sky Blues' first win in four games by curling in two brilliant free-kicks in the last four minutes to condemn the Dons to a third straight defeat.