Frankie Sawyer came off the bench to score his 21st goal of the season as Oaks claimed back-to-back wins to move back into the Bostik League South East top-10.
Dan Cumber started his first game since the FA Cup defeat against Ramsgate in September after a long absence with a foot injury, while Tommy Whitnell was also among the substitutes, having missed six games with a thigh problem.
Top scorer Sawyer replaced Adrian Stone early in the second half, and wasted little time making an impression, setting up the equaliser before grabbing the winner 11 minutes from time, completing the double over Bay.
Sawyer scored a stoppage-time penalty in the win in the reverse meeting in January, and made a big impact on things again.
On the pitch for only four minutes, his low left wing cross into the box created problems for the visitors and defender Simon Kabamba put through his own net.
However having worked so hard to break the deadlock, Oaks were in front for only five minutes.
They were caught out by a quickly taken Bay free-kick and Danny Leonard slid home the equaliser.
Top scorer Sawyer shot wide soon afterwards, before hitting the winner.
Ainsley Everett’s run and chip set-up the chance, before Sawyer touched home with a neat left foot finish inside the far post.
Fellow sub Kyle de Silva went close before end.
Alec Fiddis went close twice in the first half with Bay’s Alex-Mulronney-Skinner, and Leonard having their best chances in a goalless first half.