Sevenoaks Town still have plenty of work to do to ensure they preserve their Bostic League South East status.
A seventh home defeat of the season dropped them one place to 13th in the table, leaving them 10 points clear of bottom side Greenwich Borough next visitors to Bourne Park on Saturday week.
Latest signing, midfielder Michael Aziaya made his debut, while boss Micky Collins named another newcomer Keiran Hughes on the bench after watching him impress in the reserves.
He got his chance replacing Ryan Makosini Khanye just past the hour mark and showed up well.
Oaks suffered another blow with skipper Tom Ripley now facing a ban after picking up a 10th booking of the season.
Ripley also had a first half effort ruled out for offside and Oaks also felt hard done by when the same assistant remained unmoved after loud penalty appeals for hand ball.
The complaints to Brighton referee Conal Bartlett, his fourth appointment at Oaks this season, continued as the players left the field at half-time.
Defender Josh Dorling went closest to scoring, seeing his wind assisted effort loop over Bourne keeper Patrick Lee, only to drift wide of the far post.
Both sides created few other clear-cut opportunities in a poor game, before Oaks conceded the 85th minute winner.
A move forward broke down, losing the ball just inside their own half, the visitors broke quickly, and substitute Liam Middleton finished with a low shot wide of Ben Bridle-Card to claim the points.
Bourne completed the double over Oaks and move above them in the standings.
Collins confirmed after the game that he has released Makhosini Khanye.
Mikey Dalton has joined Ramsgate, while Luke Holness’ brief stay has also ended, signing for Tooting.