The Terriers took the lead after 16 minutes thanks to Lewis O’brien’s fierce low shot past goalkeeper Sam Johnstone.
Matt Phillips equalised three minutes later before Karlan Grant put the visitors ahead after 35 minutes to take a half-time lead at the Hawthorns.
However, a turnaround in the second half saw West Brom claim maximum points when Darnell Furlong levelling matters before Phillips sealed his brace to take the lead.
Ajayi then sealed the win after heading home from Matheus Pereira’s corner as the Baggies made it eight games without losing.
Sitting fourth on the Championship log with 16 points after eight games, Bilic’s side face Queens Park Rangers in their next outing.