But after being dominated by Town’s back line, Clarke-Harris found the net three minutes from time to grab the points for his title-chasing side.
Peterborough are in the thick of the title race but Simon Grayson’s men were the more threatening team and the biggest mystery is how they managed to be so wasteful in front of goal.
Though their title challenge had stuttered in recent weeks, Peterborough controlled the majority of the first half and should have taken an early lead but their fifth-minute chance went begging.
The ball fell kindly for the division’s leading scorer Clarke-Harris 12 yards from goal. A neat turn took Harrison Holgate out of the equation and made the space for the striker to let fly.
But although it was the kind of chance you could expect a striker with 25 league goals under his belt to snap up, keeper Alex Cairns was on hand to rescue Fleetwood. He spread himself well and somehow got in the way of the Posh hitman’s finish.
That chance aside, Clarke-Harris was kept relatively subdued by the three-man Town back line, led impressively by captain Callum Connolly.
For the opening half-hour, the hosts offered precious little going forward, but once Ged Garner had finally forced Posh keeper Christy Pym into making a save they began to show greater confidence and started to put some attacks together.
And they should have made more of two openings at the end of the half to take a lead into the break.
Moments after referee Ben Speedie succumbed to a calf injury, fourth official Graham Salisbury taking over the whistle, Garner spurned a fantastic close-range chance.
As the ball bounced around the Posh box, the ever-busy Jordan Rossiter reacted quickest and prodded it to Garner.
But just a few yards from goal, the striker somehow only managed to knock it straight into Pym’s grateful hands.
Darren Ferguson will have breathed a sigh of relief at the final action of the half, when Wes Burns raced onto another loose ball, resulting from Garner’s shot being blocked by a defender. But his finish from similarly short range cleared the bar – a huge let-off for Peterborough.
In the early stages of the second half, the Cod Army’s more patient approach was paying off, with Clarke-Harris still unable to shake off his shackles and Burns looking the most likely to create something when the hosts progressed upfield.
It was the man on the opposite flank, Danny Andrew, who had the best opportunities of the second half, either side of Sam Finley’s long-range thunderbolt that Pym managed to parry to safety.
The attacking left-back blasted high over the bar after Dan Batty’s cross was headed his way, and then sent a free-kick inches past Pym’s post.
Andrew’s best effort – a fizzing drive, came 15 minutes from time and would have been a worthy winner.
Fortunately for the promotion-chasers, centre-back Frankie Kent got the merest of touches to deflect it on to the bar and out for a corner.
And just as the game looked sure to end goalless, a free-kick on the edge of the Town box gave Clarke-Harris the chance that he grabbed with both hands, his low drive fizzing across the turf and inside the post.
It was a heart-breaking moment for a wasteful Town and served to bolster second-placed Posh’s title credentials.
Fleetwood: Cairns, Hill, Connolly, Holgate, Burns, Batty, Rossiter (McKay 90), Finley (Camps 74), Andrew, Garner (Saunders 74), Vassell; Subs not used: Coleman, Donacien, Biggins, Rydel.
Peterborough: Pym, Thompson, Kent, Beevers, Butler, Brown (Taylor 62), Reed (Hamilton 90), Ward, Szmodics, Burrows (Dembele 62), Clarke-Harris; Subs not used: Eisa, Gyollai, Kanu, Mason
Referee: Ben Speedie.
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