Salisbury City scored two late goals to inflict a first defeat of the season on Nuneaton.
The hosts broke the deadlock on 73 minutes when James Armson's cross was turned in by Louis Moult.
Ben Wright equalised with a penalty, awarded after Gavin Cowan had brought down Dan Fitchett in the box.
And the Whites snatched a winner when Elliott Frear drilled home with his left foot to extend his side's unbeaten run to seven games.
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Salisbury City manager Mikey Harris told BBC Wiltshire:
"What a fantastic level of resilience today. We fought back from 1-0 down and I don't feel we deserved to go 1-0 down. I think we just shaded the game.
"Winning away games are like gold-dust. Credit to the team today, I thought it was a fantastic team performance.
"I'm just over the moon that we've come here and picked up three points against the in-form team and the team that were top of the table."