Banbury picked up three valuable Dr Martens Eastern Division points thanks to two goals in the last minute.
Matty Gooderick was out of luck as home keeper Lee Brooks pushed his shot on to the post and Brooks then made another great save when he tipped away Les Phillips's 20-yard drive.
Wisbech took the lead in the 24th minute against the run of play as Sean Keeble headed past debutant keeper Simon Tricker, who had no chance.
Kicking against the strong wind in the second half, Banbury struggled to make headway.
Manager Kevin Brock came on for his first taste of Dr Martens League football with 15 minutes left, but just when it looked too late, they were rewarded for their persistence in the last minute.
Wisbech were caught offside and a quickly taken free kick was touched on by McKay into the path of Gooderick, who angled his shot over the advancing Brooks.
Banbury's travelling supporters went into raptures just 40 seconds later when an almost identical move saw Gooderick chip the ball over Brooks again to snatch the winner.
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