The Vanarama National North leaders suffered a setback in their title charge with this third defeat of the season.
The Coasters looked set for a comfortable afternoon in Ashton-under-Lyne when Brendon Daniels opened the scoring with a wonderful strike only for two quickfire goals to give the hosts a half-time lead.
Danny Rowe levelled the scores in spectacular fashion but a defensive error allowed Ryan Hall to seal the points.
Manager Dave Challinor made one change as Fylde returned to action after a two-week break, James Hardy replacing Bohan Dixon.
Curzon debutant Matthew Warburton set the tone with a full-blooded challenge on Dan Bradley in the first minute and received a booking.
Bradley saw the first sight of goal when he cut inside from the left but his wicked strike was palmed away by goalkeeper Hakan Burton.
The stopper went from hero to zero seconds later, when he bizarrely punched clear from a back-pass and conceded a free-kick, though Danny Rowe powered his strike into the wall.
The deadlock was broken after 10 minutes with a goal of real quality.
Intricate passing around the Curzon area culminated in Hardy backheeling the ball to Daniels, who took a touch and curled a delightful effort into the corner.
The hosts had to wait until the 20th minute for their first shot of note, Connor Hampson’s dipping effort narrowly clearing the crossbar.
The Coasters were awarded a dangerous set-piece on the edge of the box after Daniels was felled but Rowe fired high and wide.
Cummins was presented with a glorious chance to level shortly before the half hour but his free header from a corner was glanced over.
There was a contentious moment when Macauley Wilson went down under a challenge from Joe Guest but the Blackpool loanee was booked for simulation.
Curzon equalised against the run of play on 38 minutes, when a slide rule pass found Guest and he put the ball on a plate for the lurking Cummins to roll home from inside the six-yard box.
A shock turnaround was complete less than 90 seconds later. Cummins flicked a long ball on to Warburton, who beat Tom Kennedy for pace before coolly slotting the ball past keeper Rhys Taylor.
Cummins could have extended the lead further shortly before the break but slashed a strike over.
Challinor brought Richie Baker on for Josh Langley for the second half, switching to three at the back and wingbacks.
Daniels and Connor Hampson booked for mistimed tackles in a scrappy start to the second period.
James Baillie raced down the right and square the ball for Chris Rowney to side-footed narrowly wide.
The hosts were enjoying the better opportunities and Warburton should have done better with a free header at the back-post.
Caspar Hughes harmlessly headed into the arms of Burton, then out of nowhere Fylde equalised on 68 minutes, when Rowe rifled a thunderous shot from the left in off the crossbar from 25 yards.
However, with 11 minutes to play a mix-up at the back put the home side back into the lead. Dom Collins’ pass back to Taylor was short and the lively Hall nipped in to poke the ball past the helpless keeper.
Bradley’s ambitious strike from distance cleared the bar as the clock ticked down, then Rowe went on the hunt for his second when he twisted and turned on the edge of the area before drilling a low strike into the keeper’s arms.
Fylde’s first defeat of 2017 enabled Kidderminster and Chorley to cut their lead to six points, though the Coasters have a chance to restore their nine-point cushion at home to Alfreton Town on Tuesday.
Manager Dave Challinor admitted his Fylde side could have no complaints about losing after conceding some “embarrassing” goals.
“If you concede goals in the manner we did you don’t deserve to win any game.
“I wouldn’t say their two goals affected the team because we got back into the game, but conceding goals like that is embarrassing, even at kids’ level.
We spoke an awful lot in training about one goal conceded not becoming two and that was the case.
“It was a poor game. I don’t think we deserved to win.
“There was nothing in the game and we got back in it through a whopper from Rowey (Danny Rowe). To be honest, after that I’d have taken a draw because we weren’t great.
“You could tell that a couple hadn’t trained because they’d been out with niggles.
“Rowey and James (Hardy), who hadn’t played for a month, looked a bit rusty and going forward we weren’t as potent and effective as we could be.
“But you can’t concede in the manner we have. They were horrific goals.”
DANIEL AGNEW and CHRISTOPHER COUGHLIN
AFC Fylde: Taylor, Wilson, Langley (Baker 46), Collins, Kennedy, Bond, C. Hughes, Hardy, Bradley, Daniels (M. Hughes 77), Rowe; Not used: Thompson, Dixon, Williams.
Curzon: Burton, Baillie, Guest, Hunt, Shaw, Stott, Hall, Hampson, Cummins, Warburton (Howard 71), Rowney (Wright 88); Not used: Ennis, Mason, Tomsett
Ref: Aaron Jackson; Att: 341