Arsenal's on loan midfielder Jordan Fowler was dismissed seconds after half-time for a second yellow card that manger Roy McFarland thought was harsh.
To add to Chesterfield's sense of injustice, Adam Boyd scored minutes later and that was enough to extend the visitors unbeaten run to 12 matches.
But they had to dig deep as Chesterfield threw everything at them with Wayne Allison testing the Hartlepool defence in the air.
Wayne Allison struck a post and also went close with a late header, but Hartlepool held on to hold their place in the playoff zone.
They would have had a more comfortable afternoon if Adam Boyd had not wasted the sort of chance he normally puts away.
Joel Porter sent him through on goal in the 7th minute but Boyd failed to make telling contact and Carl Muggleton saved easily.
Porter was also wasteful when Boyd set him up in the 36th minute when he fired wide, with only Carl Muggleton to beat.
Those misses could have proved costly but Boyd finally hit the target in the 55th minute.
His first shot was charged down but he was quickly onto the rebound and from 12 yards squeezed a low right foot shot past Muggleton.
Chesterfield piled forward in search of an equaliser with substitute Tcham N'Toya-Zoa forcing Dimitrios Konstantopoulos into a diving save before Wayne Allison headed against the foot of a post.
An equaliser always looked to be possible despite the solid nature of Hartlepool's defence and Wayne Allison will be disappointed with the header he put over the bar when Mark Allott crossed from the right with four minutes remaining.