The defeat broke the unbeaten run of Manager Thomas Tuchel who took over from club legend Frank Lampard.
It was broke the 14-match unbeaten run of the club.
Chelsea drew the first blood through Pulisic in the 27th minute.
But things went bad when Thiago Silva received a straight red card.
West Brom took the driver seat with goals from Costa Pereira (45’+2minutes, 45’+4minutes), Robinson (63’minutes, 90’+1minutes), Diagne (68’minutes) before Mount reduced the deficit in the 71st minute.