A Jamie Cureton goal handed the hosts the half-time lead but Antoni Sarcevic levelled from the penalty spot shortly after the break before Josh Morris drilled home the winner.
Cureton's 32nd-minute strike was the only chance of note in a dismal opening period. Fleetwood failed to deal with a long throw into the area and after Matt Richards and Harry Williams had been denied, the latter by an excellent Chris Maxwell save, Cureton blasted the ball home from eight yards out.
Fleetwood lifted their game after the break and were back on level terms after 55 minutes when Richards fouled Iain Hume just inside the penalty area and Sarcevic made no mistake from the spot.
Morris was on hand to score his first goal for the Cod Army with a well-struck 65th minute volley before the home side pushed for a late equaliser.
Visiting goalkeeper Chris Maxwell did well to keep out a Sido Jombati free-kick and a Steve Elliott header while a Cureton strike was cleared off the line by Jon Parkin.