Wisbech leapfrogged Sudbury and moved out of the London 3NE relegation zone with a vital win.
Tries from Will Pettit (2), Joe Barfoot (2), Mark Law, Shane Vickers and Ben Chapman plus three conversions from Mark Laws edged them towards safety.
Captain David Wadsley said: 'We have come together as a team hopefully when it counts. The true test is when the chips are down.
'We showed our true spirit and came out fighting from the first whistle. Performances like that are exactly why we should be in that league.'
The victory, Wisbech's second on the bounce, has moved Cliff Humphreys' side four points above the drop zone with four games left.
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