Fylde are still searching for their first win of the season as they went down to their third defeat in a row in National League One
Blackheath took an early lead at the Woodlands with a penalty by Leo Fielding.
But Fylde's response was immediate, Dave Fairbrother setting up a try for Greg Smith on his debut. Smith converted his own touchdown.
On 36 minutes Blackheath regained the advantage with a try from Chris Knight, goaled from wide out by Fielding.
In the second half Tom Baldwin extended Blackheath's lead with a try converted by Fielding, who then landed a penalty to take the score to 20-7.
But this was the signal for a fightback by the home side.
Replacement Anthony Bingham dodged over in the corner for a try before man-of-the-match Fairbrother crossed for a touchdown to reduce the arrears to 20-17.
Markus Bircham scored on 70 minutes to make it 25-17 to Blackheath.
That set up an exciting finale - Scott Armstrong scored a last-ditch interception try, goaled by Smith to reduce the margin to one point, but it was too late for Fylde to get their head in front in a closely fought encounter.
The consolation for Fylde was they picked up two bonus points.