A 75th minute strike from Phoenix striker Michael Power saw the visitors move into the Ryman North play-off positions while severely denting the Planters' own hopes.
In a tense, evenly contested game both sides went close to opening the deadlock before the break.
Adam Hipperson hit the post for the hosts and Christy Finch headed over as Hipperson returned the rebound, while Christie Pattison twice went close for the visitors, heading over early on and poking a shot wide just before the interval.
The second half was a disjointed affair, with two intervals caused by a partial floodlight failure not helping proceedings. Phoenix got the winner when Power fired home first time from the edge of the area, giving Andy Wilton no chance.
Norwich United: Wilton, Shipley, Brown, Mason, Wones, Watts, Radomski (L Jackson 72), Speller, Hipperson, Henery (Stewart 60), Finch.
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