Gary Rowett's side were made to work for a point at Victoria Park as they head into Christmas in the top five in League Two.
Matty Palmer headed over from close range before the Brewers took the lead in the 18th minute.
The visitors should have been two-nil up five minutes later but Palmer screwed wide from a good position.
Albion were reliant on Edwards when he cleared a goalbound Andy Monkhouse effort off the goal-line before the break.
Dean Lyness preserved the lead when he saved well from Luke James before Monkhouse had a second effort hooked off the line, this time Ian Sharps performing heroics.
However, Pools deservedly levelled after 68 minutes. Substitute Brad Walker had been on the pitch for just two minutes when he curled home a confident first-time shot from 18 yards.
And James almost won it for Pools in the late stages, winning the ball on the touchline and racing into the area before shooting wide.
- Sports & Recreation
- Andy Monkhouse
- Scott Flinders