Trevor McCreadle opened the scoring after only six minutes but Hornets had a long and nervous wait for further success.
The visitors hit the woodwork twice in the latter stages of the game before an 86th-minute own goal by Laurence Harvey clinched a precious three-point haul for the hosts.
It arrested their recent collapse into the relegation fight, lifting them above Walton Casuals into 20th place. Three Bridges, despite their excellent form of late, find themselves four points adrift at the bottom.
The other game in the division was a Kent derby at Herne Bay where Hythe, who needed a win to move into third place, had to settle for a 0-0 draw.
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