The Pilgrims trailed inside 22 seconds courtesy of Junior Mondal's fine left-footed finish but probed away and deservedly levelled with seven minutes to play when Connor Dimaio became the first United player to score at the Jakemans Community Stadium.
Dimaio, Jordan Burrow and Tom Platt were all on target in the shootout, with Fitzsimons saving to deny Danny Philliskirk and Luke Brennan, before Garner delivered the winning touch with United's fourth penalty.
United’s afternoon got off to the worst possible start when Jack Sampson flicked a quick throw-in into the path of MONDAL to arrow a low drive beyond Fitzsimons’ dive.
The Pilgrims gradually responded to their early setback and went close when Luke Shiels headed over the bar from a Joe Leesley set-piece delivery.
Fitzsimons made a good save to deny Kurt Willoughby as Fylde chased a potentially match-clinching second goal midway through the first half.
Pierce Bird, making his second United ‘debut’ following his loan move from Eastleigh, should have scored after meeting Leesley’s corner, but nodded wide.
United were markedly the better side after the break, but their clear-cut chances were at a premium. Fraser Preston wasted one such opportunity after waltzing through one-on-one.
The Pilgrims finally levelled in the 83rd minute when DIMAIO played a one-two with Burrow before bursting into the penalty area and bending a fine curling effort beyond Fylde’s debutant keeper Lewis Thomas.
There was still time for Tom Platt to make an outstanding block to thwart Luke Conlan, as Fylde threatened to nick the tie at the death.
Philliskirk and Brennan were denied by fine Fitzsimons saves, either side of successful conversions from Jordan Lussey and Nathan Shaw, as Burrow, Dimaio, Platt and Garner fired the Pilgrims to glory.
Boston (4-2-3-1): Ross Fitzsimons; Matt Tootle (Tyrell Warren 82), Luke Shiels, Pierce Bird, Scott Duxbury (Scott Garner 75); Paul Green, Tom Platt; Fraser Preston, Terry Hawkridge (Connor Dimaio 75), Joe Leesley; Jordan Burrow. Sub (not used): Peter Crook (gk).
AFC Fylde (4-4-2): Lewis Thomas; Reagan Ogle, Nathan Pond, Alex Whitmore, Luke Conlan; Junior Mondal (Luke Brennan 90), Danny Philliskirk, Jordan Lussey, Ben Tollitt; Jack Sampson (Jack Sanders 80), Kurt Willoughby (Nathan Shaw 66). Subs (not used): Luke Burke, Liam Nolan, James Stanley, Jack Byrne.
Referee: Matthew Scholes.
Attendance: Behind-Closed-Doors.
Photography: Russell Dossett.