They needed extra-time to do it after looking as if they would win in 90 minutes, but a last-ditch goal by the Baggies brought what became just a temporary reprieve as Hartlepool scored twice in three minutes just before the end of the first half of extra-time.
Pool more than matched the Baggies in a goalless first half, creating the better chances in an end-to-end game full of flowing football.
Joel Porter had a headed goal disallowed for offside on 28 minutes, and on the half-hour Andy Monkhouse blasted a close-range shot high over the bar as the Baggies struggled to clear.
Roman Bednar was offside as he slotted the ball home for West Brom on 34 minutes, and two minutes later the Baggies record signing Borja Valero was close to marking his debut with a goal, but his shot was just wide.
The home team took the lead on 61 minutes when Gary Liddle robbed defender Leon Barnett on the left of the area and crossed low for Porter to stab the ball in from close range.
But with three minutes left of normal time, the Baggies clawed their way back into the game as Robert Koren curled a brilliant 25-yard shot into the top corner.
Hartlepool survived three scares in extra time as efforts from Luke Moore and Jonathan Greening went close before Craig Beattie's free-kick hit the home bar.
But the game was won in three minutes, sub David Foley making it 2-1 with an angled shot after his first shot was blocked, and fellow sub Richard Barker heading the third after a left-wing cross from another home sub, Matty Robson.
West Brom couldn't produce another comeback, and Hartlepool finished up deserved winners.