The former Brentford forward, partnering Wimbledon's 20-year-old leading scorer in the absence of Efan Ekoku among others, headed the decisive goal five minutes into the second half.
It was billed as the "new Wimbledon" against the real McCoy, but long passages of the match were curiously lacking in passion. Until Leicester's quest for a late equaliser, it was as if neither set of players wanted to commit themselves for fear of being suckered by the other.
Even Wimbledon's formation was deceptive, with the deployment of Michael Hughes as a third attacker designed primarily to keep Leicester's tall centre-backs busy and restrict the team's effectiveness at set-pieces.
The consequence was some numbingly sterile football which ultimately forced the Leicester manager, Martin O'Neill, into a tactical rethink.
O'Neill's cunning plan was to switch to 4-3-3 with Ian Marshall pushed into attack and Pontus Kamark assigned to shadow Michael Hughes, but though Marshall soon tested Neil Sullivan with a looping header, the change failed to achieve the desired result.
Indeed, Wimbledon soon went ahead. Goalkeeper Pegguy Arphexad kept out one Gayle header, but was found wanting in the 50th minute.
Arphexad's recent form had been good enough to allow the United States goalkeeper, Kasey Keller, to recover from jet lag on the bench after his latest international mission. But Keller would have expected to have dealt more effectively with the cross from which Gayle scored.
Cort's cross from the right soared high above the Frenchman and when Gayle made powerful contact with his head at the far post the ball was over the line before the goalkeeper could get a hand on it.
This was a second critical error within a couple of minutes on the part of the home side, for whom Steve Guppy had managed to shoot over Sullivan's crossbar from barely three yards moments earlier.
As Wimbledon dug in, Leicester abandoned their earlier caution, but Marshall missed a second chance to exploit his power in the air by heading straight at Sullivan and then Ben Thatcher launched a fierce tackle to deny Emile Heskey as Leicester's declining form stretched to seven matches with only one win.
Leicester City (3-5-2): Arphexad; Prior, Elliott, Marshall; Kamark, Parker (Savage, 76), Lennon, Izzet, Guppy; Heskey, Claridge (Walsh, 76). Substitutes not used: Fenton, Campbell, Keller (gk).
Wimbledon (4-3-1-2): Sullivan; Cunningham, Perry, Blackwell, Thatcher; Ardley, Jones, C Hughes; M Hughes; Cort, Gayle. Substitutes not used: Solbakken, Reeves, Jupp, Clarke, Heald (gk).
Referee: M Riley (Leeds).Reuse content