The first meeting between the two clubs since 1948 turned out to be an absolute thriller as the Spireites twice came from behind at the Technique Stadium to lead through Armando Dobra's double.
But just when it looked as though they would hold out for a famous victory against a team 66 league places above them, Brandon Thomas-Asante broke their hearts at the death to earn a 3-3 replay for the Championship visitors.
West Brom opened the scoring in just the second minute as Karlan Grant got in behind down the left and cut the ball back Thomas-Asante, who lashed a first-time effort into the roof of the net.
However, Chesterfield hit straight back when Jeff King took his time to chip a cross to the far post that was nodded back across goal by captain Jamie Grimes for Tyrone Williams to knock in from close range.
There was hardly time to draw breath in what was a fantastic first half, and the Baggies restored their advantage in the 17th minute.
An excellent pass by Adam Reach put Grant through on goal and although Ross Fitzsimons got a touch to his shot he could not prevent the forward from scoring his first goal since August.
The Spireites responded well again and almost equalised for a second time when Liam Mandeville's poke towards goal from King's cross was just about tipped away by David Button.
Deservedly, the hosts were level at 2-2 after 36 minutes when Mandeville's cut-back from the right found Dobra unmarked to side-foot into the top corner.
Chesterfield kept pressing and, five minutes later, were in front for the first time - a lead they retained into half-time - when Dobra hammered a rebound from Joe Quigley's saved shot high into the net.
West Brom turned up the pressure in the second half and substitute Daryl Dike almost sneaked an equaliser when his shot from inside the six-yard box was blocked during a scramble following Reach's free-kick.
Dike had another chance with 10 minutes left when the American was played in by Jayson Molumby, but Fitzsimons beat his powerful effort away.
Thomas-Asante had already had a header saved by Fitzsimons in stoppage time before he eventually came to his side's rescue by nodding Taylor Gardner-Hickman's chipped ball into the box past the stranded goalkeeper.