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…
7. Callum Connolly - 8/10
Connolly being Connolly. Slotted in well back in midfield but also did his job well at right-back in final stages. Photo: CameraSport -Alex Dodd
8. Theo Corbeanu - 7/10
Took his first goal in tangerine well, slotting home calmly after pouncing on a mistake. Helped press from the front. Photo: CameraSport -Alex Dodd
9. Josh Bowler - 8/10
Didn’t see much of the ball early on but thrived in the second-half after being given more freedom in a central role. Photo: CameraSport - Dave Howarth
10. Shayne Lavery - 8/10
Worked tirelessly, forced mistakes and deserved his goal for effort alone, although he did lack a bit of quality in the final third. Photo: CameraSport -Alex Dodd
11. Jerry Yates - 8/10
Produced an instinctive finish to complete the comeback and earn Pool a point. Delighted he’s broken his duck. Photo: CameraSport - Rich Linley
12. SUB: Gary Madine - 7/10
For Corbeanu, 64 Game changer? Provided Pool with an outlet and came close with two chances, sweeping wide and almost reaching a Bowler cross. Photo: CameraSport - Dave Howarth