An injury-time header from Lee Gregory was enough to earn the home side all three points after Jack Hunt’s first-half effort was cancelled out by Ayoub Assal.
The Owls were left frustrated for large periods and struggled to break down their visitors, who had new manager Mark Bowen in the dugout for the first time.
But Gregory’s tenth goal of the season sent Hillsborough into raptures and helped put daylight between Sheffield Wednesday and Oxford United in seventh.
Here’s our player ratings after another important win.
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Sheffield Wednesday's players celebrate Jack Hunt's goal. Photo: Steve Ellis
2. Bailey Peacock-Farrell - 6
No chance with the goal and had little to do until being called into action late on when he produced a brilliant low stop to deny Wimbledon the lead. Photo: Steve Ellis
3. Dominic Iorfa - 6
Given a tough test by Wimbledon's attackers, who got the better of him once or twice during a tough afternoon. Photo: Steve Ellis
4. Harlee Dean - 6
Brilliant last-ditch header prevented Wimbledon from taking the lead at 1-1. Booked late on for bad-mouthing the referee in frustration just before the winner. Photo: SWFC