Neil Critchley’s side went into the break two goals down, but a Sonny Carey brace inside the opening five minutes of the restart saw the Seasiders pull level.
A Shayne Lavery strike did put the visitors ahead, before Jack Marriott equalised in the closing stages with his second goal of the night.
Blackpool had the first clear chance of the game, with Jordan Rhodes smashing the crossbar with an effort from the edge of the box.
Meanwhile, Carey forced a save from Jay Lynch, after producing a fierce shot from distance.
Down the other end, Dan Grimshaw was also worked a couple of times, before Fleetwood opened the scoring in the 14th minute.
The visitors couldn’t stop Promise Omochere as he made a powerful run down the right side, with the midfielder finishing off the move with a left-footed finish.
A second goal soon followed for the home side, after another piece of poor defending.
Following a free kick into the box, a close-ranged shot from Omochere was initially parried by Grimshaw, with Marriott waiting to score on the rebound.
After the break, Blackpool didn’t have to wait too long to find the back of the night, and were level at 2-2 within five minutes of the restart.
Carey was on hand on both occasions on the edge of the box.
The midfielder curled his first goal into the bottom corner, before smashing the second one past Lynch.
With momentum truly swinging in Blackpool’s favour, the Seasiders took the lead in the 66th minute.
Rhodes played the ball through to half substitute Shayne Lavery, who slotted past the keeper at the front post.
The Northern Ireland striker certainly made a positive impact off the bench, alongside the in-form Karamoko Dembele.
In the final minute of normal time, Fleetwood pulled themselves level, with Marriott beating Grimshaw with a superb strike from the edge of the box.
Blackpool did have a late opportunity to snatch all three points, but the ball was just about cleared off the line following a great save by Lynch.