Substitute Cureton struk the only goal, the 249th of his prolific career, in the fourth minute of injury time to earn the Robins their first victory at the Abbey Business Stadium in Sky Bet League Two this season.
"We got what we deserved in the end because we showed resilience and character and we've not been playing our best recently, so to come away with a good result against a decent side is pleasing," Yates said.
"We kept plugging away, showed we are together and we showed we have goalscorers here and when we keep clean sheets and look a lot more organised we have a chance of winning games.
"Jamie Cureton still had a lot to do with the chance after he got himself back onside by half a yard and he was on his bike, which is a lesson for all our strikers.
"It bounced awkwardly for him but he had the composure to put in a great finish and our performance deserved a win."
Yates was confused by referee Darren Drysdale's decision to award Cheltenham a second half penalty before changing his mind and giving Wimbledon a free-kick.
"I won't criticise the referee too much because we won the game, but he must be a relieved man," Yates said.
"He gave us a penalty and then changed his mind. I don't know why that happened, but we got there in the end."