The Tangerines had it all to do at the break as they trailed 3-1 after Theo Corbeanu had pulled Michael Appleton's men back into the game.
The 20-year-old forward's finish was sandwiched in-between Nathan Tella's double for the hosts with Josh Brownhill breaking the deadlock early on.
Vincent Kompany’s side appeared to be heading for a first win since the opening day of the season away at Huddersfield Town, but they were denied by a spirited comeback from the visitors.
Shayne Lavery and Jerry Yates converted from close range in the space of just three minutes — with a quarter-of-an-hour left to play — 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 by referee Keith Stroud.
Here are Matt Scrafton's player ratings…
13. SUB: James Husband - 7/10
For Thompson, 76 Produced some vital challenges and headers late on as Burnley pressed for a dramatic last-gasp winner. Photo: CameraSport - Dave Howarth
14. SUB: Sonny Carey - 6/10
For Gabriel, 76 Thought his cynical challenge for the red card probably warranted a red card, but I can see why he did it. Photo: CameraSport - Rich Linley
15. SUB: CJ Hamilton - 7/10
For Lavery, 76 Almost made an instant impact off the bench after being denied by the keeper seconds before Pool’s equaliser. Photo: CameraSport - Dave Howarth
16. SUB: Matty Virtue - 6/10
For Yates, 89 Put in a physical shift late on as Blackpool desperately attempted to see out the final eight minutes of stoppage time. Photo: CameraSport - Dave Howarth