The Gulls beat Barnet 3-2 in their relegation 'six pointer' and move up to 20th in League Two, but just one point above the relegation zone with two games to go.
Elliot Benyon, Billy Bodin and Brian Saah scored the goals at Plainmoor.
Plymouth Argyle won 2-1 at Chesterfield thanks to first-half goals from Joe Bryan and Curtis Nelson. They're up to 17th.
In League One, Lee Johnson was victorious over his father Gary as Oldham beat Yeovil 1-0 at Boundary Park.
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He's been Bristol City's head coach for 9 months, now Lee Johnson signs a new contract keeping him at Ashton Gate until 2020.