He the scoring with a 22nd minute penalty and he doubled the lead six minutes later with a header from Adbul Osman's cross.
The substitute Kevin Nolan did pull one back late on for the hosts, but it proved no more than a consolation on a poor night for Gary Megson's side.
Hartlepool - who knocked out Scunthorpe in the first round of the competition - turned West Brom's early-season woes into a crisis as they dumped the Premier League new boys out of the competiton.
They needed extra-time to do it after looking as if they would win in 90 minutes, but they recorded a 3-1 victory.
Goals in either half from Anthony Elding and Byron Moore booked Crewe a place in the third round draw.
While Brian Wilson's stunning 30-yard strike 11 minutes from time set up a tense finish, the Alex were worthy victors over Championship opposition.
Leeds United coasted into the third round after totally outplaying Championship opponents Crystal Palace in a 4-0 success at Elland Road.
Jonathon Douglas opened the scoring, Jermaine Beckford netted his fifth goal in as many games, Argentine Luciano Becchio crowned an impressive display by scoring the third and substitute Enoch Showunmi added the fourth.
Oldham Athletic, Yeovil Town, Cheltenham Town, MK Dons and Carlisle United were all beaten.