Defender Steve Elliott and midfielder Darren Carter were on target for the Robins before Dons substitute Brennan Dickenson reduced the arrears after the hour.
"Psychologically, from having conceded a couple of late goals in recent games, this is a massive win," said Yates. "We have conquered it and we know how to win now. We have lots of tough games coming up but we can use this to our advantage.
"I thought we played some really good stuff but made it difficult for ourselves by conceding.
"In seven games we have conceded one goal - two at Accrington - and I think (goalkeeper) Scotty (Brown) and the boys deserve better but we will keep working to put it right."
Yates admitted Carter was on the verge of being substituted before scoring what proved to be the winner.
"Darren rocked his ankle before half-time and he didn't start the second half particularly well," he added.
"But I always find that if you get someone to take their shirt off something happens. He must have had an inkling that he was coming off but he showed his class with a great goal.
"I thought Michael Hector and Steve Elliott were outstanding but it was a good team performance perhaps marred by conceding that one goal and putting the crowd on edge for the last 15 or 20 minutes."
- Sports & Recreation