Fylde accelerated into a 14-0 lead but fell off the pace against purposeful London hosts.
A third Fylde try in the 61st minute brought them right back into the contest but Park eased away with two late tries to secure maximum points.
Fylde scored first as Ben Vernon finished off a smart move well after 14 minutes, Greg Smith converting.
Nine minutes later, all-action no.8 David Fairbrother celebrated his return after a month out by powering over for another good try, Smith again adding the extras.
Fylde full-back Warren Spragg was sinbinned by referee Daniel Parrott two minutes later and Park took due advantage when winger Josh Watkins sneaked over to claim a try in the 31st minute.
Fly-half Harry Leonard kicked the conversion,then six minutes later put a grubber-kick through the Fylde defence which resulted in a 60-metre breakaway try by centre Rhys Crane.
Fylde maintained their lead by charging down Leonard’s conversion attempt, and although Smith missed a penalty just before the interval Fylde retired to their changing room 14-12 ahead.
With the wind behind them, Park took the lead in the 47th minute when Watkins sniped over for his second try after a series of drives.
Leonard converted this and added a penalty in the 57th minute to extend their lead to 22-14.
Fylde hit back with a try from a rolling maul. They drove the home pack backwards and lock Jack Turley was last up in the pile of bodies. Smith missed the conversion but Fylde trailed by only three points.
They should have regained the lead moments later but an excellent chance went begging, then Park took control as Jamie Harries burst through Fylde’s defence for a crucial try, improved by Leonard, on 72 minutes.
Fylde ended the game with 13 men as prop Simon Griffiths was followed to the sin-bin two minutes later by Fairbrother.
This enabled replacement prop Ali Wade to pick a neat line to score the final try.
Fylde have lost all but one of this season’s 12 away games in National One, but like several others this could have gone the other way but for some errors and bad decisions.
With four games of his tenure as head coach remaining, Paul Arnold said: “I’m very disappointed not to come away with anything from the game.
“When we were only three points behind with 10 minutes or so to go we spurned a glorious chance and from that position a good Park side punished us.
“There were a lots of positives to take from the performance but we have to cut out the basic mistakes and stop putting ourselves under pressure.
“I can’t fault the work rate or commitment of the whole squad. I give a special mention to the pack, who were excellent throughout, especially Fairbrother, who was everywhere.”
Fylde drop a place to13th and face Old Albanian at the Woodlands on Saturday.
Fylde: Spragg; Bailey, Wilkinson, Briers, Armstrong; Smith, Dever; Pope, Burtonwood, Lewis, Gray, Turley, Rogerson, Vernon, Fairbrother; Replacements: Wild, Gregory, Lamprey, Griffiths, Nicholls.