The game's turning point came on the hour when defender Chris Westwood tangled with Baggies substitute Scott Dobie and was shown a straight red card when few people in the crowd had even spotted an offence.
To rub salt into Hartlepool's wounds, another West Brom substitute, Neil Clement, hammered the 20-yard free-kick into the top corner of the net.
Until that point Hartlepool had more than matched their first division opponents.
They had been inches away from taking the lead on 12 minutes when Mark Tinkler's long-range shot after a short free-kick was headed against his own bar by Albion defender Thomas Gaardsoe.
From the rebound Marco Gabbiadini's header was brilliantly saved by visiting keeper Russell Hoult.
But Pool did go ahead in the first minute of first-half stoppage time, Paul Robinson stroking his penalty into the bottom corner after Gaardsoe was adjudged to have handled in a crowded penalty area.
West Brom were rattled, but they got the lucky break they needed on the hour as Westwood saw red and then grabbed their equaliser, before growing in confidence as the match went into its last quarter.
Their winner came ten minutes from the end when Dobie got away on the right after a long clearance and Rob Hulse scored from close-range opposite the near post.
And despite a frantic finish, Hartlepool's ten men could not take the game into extra-time.
Hartlepool: Provett, Barron, Westwood, Nelson, Eifion Williams, Strachan, Tinkler, Humphreys, Clarke, Gabbiadini, Paul Robinson. Subs: Anthony Williams, Robson, Easter, Istead, McCann.
West Brom: Hoult, Gaardsoe, Berthe, Gilchrist, Haas, Koumas, Johnson, O'Connor, N'Dour, Hughes, Hulse. Subs: Murphy, Dichio, Dobie, Clement, Adam Chambers.
Referee: P Prosser (Gloucestershire)