The visitors made the perfect start when Troy Brown headed home Matt Richards' free-kick in the fourth minute.
Cheltenham's lead was doubled eight minutes after the restart when Byron Harrison's strong run and pull back set up Jermaine McGlashan, who scored his fifth of the season.
Three goals in three stunning minutes then saw Wimbledon storm back to take the lead.
First Midson set up substitute Danny Hylton in the 68th minute for his fourth of the campaign and Cheltenham fell apart defensively.
Hylton laid the ball on for Jake Nicholson's deflected leveller a minute later before Charlie Wyke's flick-on saw Hylton race through and round Cheltenham goalkeeper Scott Brown for the Dons' third.
Cheltenham recovered composure and equalised four minutes later through Jason Taylor, but Midson struck from close range in the seventh minute of time added on with virtually the last kick of the game after Brown had flapped at a cross.