Two goals in as many minutes earned AFC Fylde a share of the points after trailing 2-0 early in the second half.
The visitors raced into an early lead through Frankie Sutherland and Josh Rees poked home the second.
However, quickfire goals from 17-year-old Serhat Tasdemir and top scorer Danny Rowe sealed a point for the hosts.
Coasters boss Dave Challinor made two changes to the side beaten by FC Halifax Town seven days earlier, with Zaine Francis-Angol returning in place of Josh Ezewele and Henry Jones replacing James Hardy.
The visitors almostled inside two minutes as frontman Brett Williams was sent racing clear but Rhys Taylor got down well to turn his low strike around the post.
Bromley went closer still a minute later, when Luke Wanadio’s powerful effort from 25 yards cannoned back off the crossbar.
A goal looked to be coming and duly arrived in the eighth minute, when Wanadio broke away down the right and delivered a low ball into the area that Sutherland tucked away at the near post.
Williams then diverted the lively Wanadio’s goalbound strike past Taylor but an assistant referee’s flag denied them a second.
Fylde were whipping balls into the box but were enjoying little luck in the final third, though full-back Luke Burke flashed one wide on the 20-minute mark as the Coasters started to raise their game.
Record goalscorer Rowe had his first opportunity of the afternoon midway through the half but headed straight into the hands of Gregory.
A big clearance from Sam Finley gave Jack Muldoon a chance to stretch his legs and find Jones but the Welshman’s shot on the turn was blocked.
The tide was turning with 10 minutes of the half to play and the unlikely figure of Francis-Angol almost levelled up proceedings when his cross from the left glanced off the underside of the bar.
The visitors took just five second-half minutes to extend their lead. Rowe’s challenge handed Bromley a corner that was flicked home far too easily by midfielder Josh Rees.
Challinor made changes as Andy Bond and Muldoon made way for youngsters Jonny Smith and Tasdemir.
Fylde were a whisker away from pulling one back on the hour. Burke floated a ball over the top to Rowe, who headed over Gregory but the keeper scrambled back to claw the ball off the line.
The visitors were almost gifted a third when Finley had his pocket picked and Wanadio raced clear, skipping past three challenges before crossing to Rees, who headed just wide.
Two crazy minutes turned the game on its head. A quick break on 67 minutes saw Jones’ shot deflected into the path of Tasdemir, who took a touch before drilling an exquisite low drive into the far corner.
And the Coasters were level when Smith played the ball into Rowe on the edge of the area and the frontman turned his man before slamming a left-footed strike into the far corner for his third goal in successive games.
Jones almost completed a sensational comeback with 15 minutes remaining, when he lashed a vicious strike narrowly over the bar from the edge of the area.
Midfielder Lewis Montrose could have nicked it for the hosts in added time but shot a foot wide from Rowe’s knockdown.
Fylde drop a place to 18th ahead of Tuesday’s visit to Macclesfield.
AFC Fylde: Taylor, Burke, Tunnicliffe, Grand, Francis-Angol, Montrose, Bond (Smith 53), Finley, Jones (McCready 82), Muldoon (Tasdemir 53), Rowe; not used: Lynch, Ezewele.
Bromley: Gregory, Chorley, Holland, Sterling, Dunne (Wynter 77), Sutherland, Raymond (Higgs 80), Porter, Rees, Wanadio, Williams (Dennis 83); not used: Johnson, Allen.
Referee: Andrew Miller