Williamson climbed off the bench with 18 minutes to go and hit the winner with 10 remaining after the Blue Square Premier side fought back from two goals down.
Vale went ahead after seven minutes when Louis Dodds' cross-field pass found Ashley Vincent, who skipped past challenges from Ed Asafu-Adjaye and Jamie Turley to place the ball to Sam Russell's left.
The visitors doubled their lead five minutes later, Vincent turning provider, taking down Ryan Burge's cross and supplying Clayton McDonald with a close-range finish.
Forest Green were stunned but fought their way back when James Norwood curled into the top corner after 34 minutes and they were level when skipper Eddie Oshodi tapped in from close range.
Rovers piled on the pressure and went close when Matty Taylor's shot was cleared off the line by McDonald but they couldn't find a winner and were made to pay when Williamson nodded home.