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…
1. Dan Grimshaw - 8/10
Not much he could have done about Burnley’s three goals, but made a vital stop at the death to ensure the point. Photo: CameraSport - Dave Howarth
2. Jordan Gabriel - 7/10
Caught out for Burnley’s second and slipped for third. But showed a great response in the second-half. Photo: CameraSport - Dave Howarth
3. Marvin Ekpiteta - 8/10
Backed off a bit for Burnley’s second, but that’s just being picky. Defended excellently despite the three conceded. Photo: CameraSport - Rich Linley
4. Rhys Williams - 7/10
Solid, a couple of shaky moments aside. Produced some vital late headers as Burnley pressed for a late winner. Photo: CameraSport - Dave Howarth
5. Dom Thompson - 7/10
Always risks a booking with his tough challenges but can’t fault his determination. Produced some dangerous crosses too. Photo: CameraSport - Dave Howarth
6. Kenny Dougall - 7/10
A little hurried in possession early on but improved as the game wore on. His blocked shot led to Pool’s late equaliser. Photo: CameraSport - Rich Linley