The Robins squandered their first half advantage as they conceded two goals in 10 second half minutes in SkyBet League Two.
Cheltenham had taken the lead through Jamie Cureton after 32 minutes and the home side were looking comfortable.
But when Matt Richards hauled down Iain Hume inside the box, Fleetwood's top scorer Antoni Sarcevic was on hand to level the scores before Josh Morris took the lead 10 minutes later.
It was the visitors first victory against the Robins in only their fourth ever competitive meeting.
Fleetwood Town made just the one change following their score draw against Morecambe last week. Stephen Jordan started ahead of Leeds United loanee Charlie Taylor who did not feature in the match day squad.
Graham Alexander opted to utilise wing-backs rather than the diamond formation he had adopted in previous weeks.
The Robins were unchanged following their 1-1 draw against Exeter. Harry Williams retained his place and made his first start at Whaddon Road following last weeks professional debut.
The young attacking midfielder was in and around the action for the entire first half and didn't look out of place drawing fouls from the visiting defenders whilst linking up well in attack.
The game took a while to get going but Mark Yates' side looked dominant as the visitors offered very little going forward.
Byron Harrison came close as he found space at the back post from a Richards corner before Cureton hooked a shot over the bar from an offside position.
The Robins were rewarded after the half hour, Craig Braham-Barrett's long throw bounced around the box before Williams eventually saw his shot saved. The keeper could only parry and the ball fell to Cureton, the striker found the bottom right corner with pinpoint accuracy to give the home side a deserved lead heading into the break.
Iain Hume came close to levelling the scores moments later as he struck against the side netting but the Robins continued their dominance as Fleetwood struggled to get a foothold in the game.
Half Time: Cheltenham Town 1-0 Fleetwood Town
It was de ja vu for Cheltenham in the second half as they swiftly threw away their one goal advantage. After almost conceding an own goal, Hume put a shot narrowly wide of goal from an offside position. The Robins looked to be struggling in defence and Matt Richards hauled down Hume on the byline to concede a penalty.
Fleetwood's top scorer had been quiet all afternoon but Sarcevic stepped up to fire a thunderous strike past Scott Brown who had dived the right way.
And just 10 minutes later, David Ball teed up Josh Morris as they split the Robins back four and Robins just poked the ball past Brown as Fleetwood took the lead.
Mark Yates made a double substitution in an attempt to claw the game back. Deering and Vincent replaced Williams and Richards.
But it was the most unlikely of players who almost drew the sides level. After McGlashan was fouled on the edge of box, Sido Jombati struck a free kick that looked destined for the top left corner. The right back denied by a fine Chris Maxwell save.
Cureton came close as he saw an effort headed behind by substitute Jon Parkin and Elliott headed narrowly wide from just six yards. But the Robins were clutching at straws as Vincent's late effort was volleyed over the bar with his back to goal.
And with five minutes of added time, Morris came close to scoring his second of the afternoon but his shot fell just wide of Scott Brown's upright.
The win guarantees a play-off spot for Fleetwood who are now within just three points of the automatic promotion spots with just three games remaining.
Full Time: Cheltenham Town 1-2 Fleetwood Town
Cheltenham Town FC (4-4-2 Diamond): S Brown; Jombati, T Brown, Elliott (C), Braham-Barrett; Noble, McGlashan, Richards (Vincent '59), Williams (Deering '59); Harrison, Cureton.
Subs not used: Roberts (GK), Brundle, Ihiekwe, Kotwica, Gornell.
Fleetwood Town FC (5-3-2): Maxwell; McLaughlin, Goodall, Pond, Roberts, Jordan; Blair, Morris, Ball (Evans '85); Sarcevic (Cresswell '83); Hume (Parkin '75).
Subs not used: Davies (GK), Murdoch, Schumacher, Barton.
Referee: Mr. Graham Horwood
Attendance: 2,890 (134 Visiting Fans)