The Clarets were well in command at the break when leading their rivals 3-1 thanks to Nathan Tella’s double.
The Southampton forward found the net in the 11th and 33rd minute following Josh Brownhill’s sumptuous opener.
Theo Corbeanu was on the scoresheet for the Seasiders in the first half, punishing an unforced error from the home side and finishing past Arijanet Muric.
Vincent Kompany’s side were heading for a first win since the opening day of the season away at Huddersfield Town, but the visitors had other ideas.
Shayne Lavery and Jerry Yates converted from close range in the space of just three minutes to level proceedings.
Both sides then ended the game with 10 men as Ian Maatsen reacted to a reckless challenge from Sonny Carey, which resulted in both players being given their marching orders.
Here are Chris Boden’s player ratings.
1. Arijanet Muric 6
The debate will go on about his involvement In Blackpool’s first goal, whether he needed to make that pass, whether it was just a poor touch from Cullen, but he will continue to take risks to find the spaces, and produced two crucial saves in the second half. Photo: CameraSport -Alex Dodd
2. Connor Roberts 6
Playing in midfield for much of the time, while trying to get up and down the line as well, and still adapting to the role. Photo: CameraSport - Rob Newell
3. Taylor Harwood-Bellis 7
Two superb passes led to the opening two goals, but part of a Burnley defence which folded after the introduction of Madine. Photo: CameraSport - Rich Linley
4. Charlie Taylor 6
Again didn’t look entirely comfortable in his new role, and frustrated fans by turning down opportunities to pass forward as Burnley looked to try and regain the lead. Photo: CameraSport - Rob Newell