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Gillingham scored three quickfire goals to turn the match against Swindon Town on its head and clinch the win.
Brett Pitman netted for the home side shortly before the interval but Oliver struck twice in a five-minute spell before Kyle Dempsey added a third.
Gillingham missed out on closing the gap between themselves and the play-offs after suffering a 1-0 defeat to Fleetwood in midweek, the only goal coming from a controversial penalty decision.
Boss Steve Evans had been unhappy with his own team too that night and suggested he would make changes. He resisted the urge and for the fifth match running named the same eleven starters.
John Sheridan’s relegation-threatened Swindon side have lost more games this season than any other and prior to Gillingham’s visit had the second worst goals against tally. If Gills were to mount a play-off push this was a game to be won.
The game lacked real quality in the first half, the Gills often wasting opportunities with crosses into the box.
Home keeper Connal Trueman didn’t have a lot to do in the first 45, claiming a header from Stuart O’Keefe and getting a vital touch on a cross from Olly Lee as he did well to wriggle free in the box.
Jack Bonham in the Gills goal wasn’t overly troubled either, comfortably taking a couple of efforts but the home side took a 41st minute lead through Pitman, taking a touch to make space before firing home. He had been played in by Jordan Lyden who had found himself with plenty of space to work in.
Evans swapped Alex MacDonald for Tommy O’Connor at the break and the Gills started the second half brightly. Early appeals for a penalty were waved away after Robbie Cundy went down in the box under pressure from Dion Conroy.
It wasn’t long before John Akinde was also introduced.
Oliver and Connor Ogilvie both had shots blocked before then Gills staged their comeback.
It was a close range finish from Oliver on 59 minutes that got the Gills back level, the Gills striker seeing the ball over the line from under the bar after Akinde’s header had come off the crossbar.
A second goal for Oliver came four minutes later, picking up a loose ball and scoring with a low angled drive from the edge of the box, clipping the near post before the ball nestled into the opposite side of the goal.
Dempsey made it 3-1 on 69 minutes, his low free-kick hitting a few bodies on the way to beating keeper Trueman.
Oliver headed a good chance over soon after and at the other end Bonham saved well from Tyler Smith, one of five Swindon subs that were made at the same time, in a desperate attempt to salvage something from the game.
Pitman went close in the last minute with a header, and the hosts wanted a penalty when the ball hit Ogilvie's hand in the box, but the Gills kept hold of their advantage to take the points back to Kent.
Swindon: Trueman, Caddis, Conroy (Curran 77mins), Pitman, Twine, Garrick, Lyden, J Grant (Payne 77mins), Thompson (Iandolo 77mins), Broadbent (Odimayo 77mins), A Grant (Smith 77mins). Subs not used: Matthews, Payne, Missilou.
Gillingham: Bonham, Jackson, Ogilvie, Cundy, Tucker, Dempsey, O'Keefe (Woods 90mins), O'Connor (MacDonald 46mins), Lee (Akinde 52mins), Graham (McKenzie 90mins), Oliver. Subs not used: Bastien, Willock, Johnson.
Referee: James Bell