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.
9. Vitinho 6
Not as effective when he has started as when he has come off the bench as an impact substitute. Photo: CameraSport - Alex Dodd
10. Jay Rodriguez 7
Involved in the opening goal and linked play well throughout, also unfortunate to be taken off when he was. Photo: CameraSport - Rich Linley
11. Nathan Tella 8
Became the first Burnley player to score twice on his first start for the club since Steve Jones in 2006, unfortunate to be withdrawn. Photo: CameraSport - Rich Linley
12. Ashley Barnes 4
His introduction changed the dynamic and the momentum swung in Blackpool's favour. Offered little on or off the ball. Photo: CameraSport - Alex Dodd