Daniel Wishart scored a late winner for Hayes and Yeading in their relegation battle against Kettering.
Luke Williams went close for the home side mid-way through the first half but his effort was saved by Laurie Walker.
Kettering could have led at half-time, but Steve Arnold produced an excellent stop to deny Nathan Ralph.
Just as the game looked to be heading for stalemate, Wishart fired in from close range to boost the Londoners' chances of survival.
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Kettering Town caretaker manager Ashley Westwood told BBC Radio Northampton:
"That's as gut-wrenching as they come.
"We've turned it around at half time. We took the game to them, we had the momentum and the better of the second half and then they have scored five minutes from the end.
"We'll dust ourselves down. We've got a game Tuesday. No-one will expect us to get anything at Southport.
"I'm asking the players to take encouragement from the way they've played."