Midson inadvertently nodded Matt Grimes's corner into his own net in the early stages of the game to give the away side the lead.
Jimmy Keohane then blasted over from 12 yards as Exeter had the better of the early chances.
However, Wimbledon slowly grew into the contest and Artur Krysiak made a smart, low save from Alan Bennett before Callum Kennedy's corner ended with a goalmouth scramble, and the Polish goalkeeper was forced to come to his side's rescue once more.
The pressure paid off when they levelled eight minutes before half time. Charlie Wyke squirmed his way past Scot Bennett and rolled the ball across the six-yard box to leave Luke Moore with a simple tap-in.
Right on the stroke of half time, Sammy Moore was shown a yellow card for a late tackle on Grimes and the youngster didn't emerge after the break.
The man who replaced him, John O'Flynn, wasted a good opportunity for Exeter 10 minutes into the second half when he smashed the ball over the bar in an unmarked position from 12 yards.
Exeter thought that they had taken the lead when Tom Nicholls pounced to slot the ball past Worner, but the flag was raised immediately.
Shortly afterwards, Nicholls sent a curling effort inches wide of the far post with the Dons goalkeeper rooted to the spot.
However, with just over 15 minutes remaining, Midson converted from Kevin Sainte-Luce's low cross to give the Wombles the victory.