Williams struck twice in the second half as the visitors came from a goal down to claim their first away win since November. It also took the Glovers four points clear of the drop zone in League One, while dropping the Chairboys back in it.
Wycombe took the lead when Matty Wichelow set up Stuart Beavon but Yeovil equalised just before the hour mark when Williams tapped into an empty net.
Williams then put the Glovers ahead when his cross missed Jon Obika and trickled in, and Kieran Agard doubled the lead by heading in Ed Upson's cross before Joel Grant pulled one back.
Johnson said: "At 1-0 down at half-time we thought we needed to liven up in attack - Andy Williams especially, up there with Jon Obika.
"I felt Andy could turn the game with his strength and we just needed to start to get midfield runners and our widemen past people. Once we started doing that we looked a force and Andy deserved his two goals."
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