Nayef Aguerd nodded West Ham into a seventh-minute lead after taking advantage of James Ward-Prowse’s inch-perfect corner kick.
Chelsea responded and deservedly levelled when 19-year-old Carney Chukwuemeka rifled a superb solo strike into the far corner for his first senior goal just shy of the half-hour mark.
The lively Raheem Sterling then earned Chelsea a penalty two minutes before half-time, but Enzo Fernandez’s low spot-kick was well saved by Alphonse Areola.
The pattern of Blues dominance threatened to continue following the break, but it was the hosts who stole in front when Ward-Prowse chalked up a second assist, releasing Antonio to surge free and thunder a sublime, low strike into the far corner.
Chelsea turned to British record signing, Moises Caicedo as he made his debut from the bench and their hopes appeared to be further boosted when Aguerd was sent off for a second bookable offence 23 minutes from time.
However, West Ham defended for their lives and then sealed the points when Caicedo brought down Emerson.
Paqueta, reportedly the subject of an FA probe into betting breaches, applied the knockout blow by converting the penalty.
Dating back to last season, Chelsea have won just five times in 31 league matches, while their only victory in their last 14 top-flight games came at Bournemouth in May.
They have also lost four successive top-flight London derbies for the first time since 1990.
Much of the blame for those dismal statistics lies with Pochettino’s predecessors Graham Potter and Frank Lampard, who struggled through a turbulent campaign that ended with Chelsea’s lowest finish since 1996.