Kay struck what proved to be the winner as the hosts overturned a half-time deficit to lift spirits after their Capital One Cup exit to Sheffield United in midweek.
Swindon were off to a flyer after six minutes when a great pass by Yaser Kasim put Michael Smith in behind the Dons defence and he slid the ball across for Jonathan Obika to tap in.
Obika almost returned the favour as Smith beat the offside trap and tried to go around David Martin, who stood his ground to make a good block.
MK Dons drew level thanks to a brilliant shot by Dele Alli, whose effort from the edge of the area flew into the top corner of the net with goalkeeper Wes Foderingham a mere spectator.
And the match was turned on its head just before the hour mark when Kay arrived at the back post to turn in Ben Reeves’ dangerous free-kick.
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