More on KentOnline
Gillingham were unable to recover from conceding a second minute penalty at Fleetwood.
Kyle Vassell scored from the spot and also struck the bar as the hosts edged an opening half of limited chances.
Fleetwood hit the woodwork again on the hour while for the Gills John Akinde was twice denied by the home keeper after the break as the hosts held on to win 1-0.
Both teams were full of confidence ahead of the match, each boasting back to back wins before their meeting at a chilly Highbury Stadium.
The Gills knew the play-off places were again tantalisingly close after a good run of form. They remain five points adrift despite the loss at Fleetwood.
It was no surprise that manager Steve Evans once again named an unchanged side.
It was the hosts who made a dream start, Vassell sending keeper Jack Bonham the wrong way from the penalty spot after referee Marc Edwards penalised Connor Ogilvie for a shove on Ged Garner in the box. It was a soft one to award.
Vassell went close moments later with a dipping effort, aided by a deflection, which bounced off the top of the bar.
Fleetwood saw plenty of the ball in the opening half but were unable to create many openings. Bonham claimed a tame low shot from Garner while at the other end Tommy O’Connor’s dipping effort flew over the bar.
Gillingham’s best chance of the half fell to Olly Lee, denied from close range by keeper Alex Cairns, after Robbie Cundy had flicked on an O’Connor free-kick. James Hill had to hook the ball clear.
Gillingham made a switch at right-back during the break. Ryan Jackson had picked up a knock and was replaced by Robbie McKenzie.
Dan Batty fired wide for Fleetwood early in the second half and it wasn’t long before Evans made another change, sending John Akinde on with 50 minutes played to join Vadaine Oliver up top for the Gills.
Akinde made an immediate impact, unsettling the Fleetwood defenders, and was denied a goal by Cairns after the keeper stuck out a boot to dent the striker.
Fleetwood struck the bar for the second time of the match when Bonham was almost caught out. The goalkeeper was out of his goal to make a clearance but could only find Jordan Rossiter and from just inside the Gills half his long-range effort hit the woodwork.
Evans continued to make changes, introducing Matty Willock and Alex MacDonald from the bench.
Cairns denied Akinde again with 13 minutes left following a shot on the turn inside the box after Oliver nodded down an Ogilvie throw. Dempsey fired over from an angle after he was played in by Akinde.
Gaps were left at the back late on for Gillingham and Bonham had to save from Madden.
Fleetwood: Cairns, Andrew, Donacien, Connolly, Holgate, Hill, Camps (Finley 84mins), Rossiter, Batty (Biggins 84mins), Vassell, Garner (Madden 66mins). Subs not used: Coleman, Burns, Rydel, S Morris.
Gillingham: Bonham, Jackson (McKenzie 46mins), Ogilvie, Tucker, Cundy, O'Keefe, O'Connor (Akinde 51mins), Dempsey, Lee (Willock 66mins), Graham (MacDonald 69mins), Oliver. Subs not used: Bastien, Morton, Johnson.
Referee: Marc Edwards