The Robins first displayed loose defending when they gave gave Alex MacDonald the chance to fire their promotion rivals in front from eight yards in the 22nd minute.
Then MacDonald turned provider four minutes later with a cross that gave the unmarked Robbie Weir the chance to find the far corner with a 12-yard header.
Cheltenham's hopes of clawing their way back into the game were in ruins when Weir met a Billy Kee cross to head his second of the game in the 48th minute.
Byron Harrison headed a stoppage time goal that was of little consolation to Yates.
He said: "I thought we were great for 20 minutes without quite having any end product. The system we played seemed to be working and the home fans were just starting to have a little moan.
"But then we gave away we three really soft goals - and you can't afford to do that against a team in such good form at home.
"The back four were all awful and I don't think anyone came out of the game with any credit.
"We let out standards slip because we're a lot better than we showed.
"Second half we created chances, but they got bodies on the line and did what they had to do to win the game."