The former Exeter striker, back on the pitch after a spell sidelined with injury, latched onto a huge clearance from Scott Brown, celebrating his 250th appearance for the club, and beat Ross Worner with an expect finish to earn the Robins their first home league win of the season.
George Francomb's angled drive had flown just over in the 23rd minute of a cagey first half.
Ex-Dons frontman Byron Harrison rose highest to meet David Noble's corner two minutes later, but it was kicked away from danger before he tried his luck with an overhead kick.
Noble set up Harrison for another chance, but he shot wide under pressure from Andy Frampton and it was then the Rotherham loanee's turn to threaten when he headed Matt Richards' cross at Worner as the first half finished goalless.
Cheltenham made the brighter start to the second half, with winger Jermaine McGlashan seeing plenty of the ball. He won a tackle with former Robins skipper Alan Bennett before exchanging passes with Harrison, but his cross evaded Gornell.
McGlashan then drew a fine stop from Worner in the 48th minute after a fine run.
Wimbledon's best chance came from an indirect free-kick on the edge of the six-yard box after Scott Brown picked up a backpass. Substitute Chris Arthur's shot after Luke Moore's touch flew just wide.
There was controversy in the final minutes after Cheltenham were awarded a penalty for a foul on Gornell, but referee Darren Drysdale then changed his mind and gave Wimbledon a free-kick before Cureton provided a late twist.