Potter has won just five of 21 games since taking charge in January and has endured a miserable start to the new campaign after a 3-0 defeat to newly-promoted Sunderland last weekend.
Lucas Paqueta’s brilliant strike gave the home side early hope on Friday, blasting into the top corner from long range, but they quickly capitulated.
Joao Pedro scored the first of Chelsea’s three goals from corners before Pedro Neto and Enzo Fernandez added to the world champions’ lead.
Moises Caicedo and Trevoh Chalobah then took advantage of a nightmare night for new West Ham goalkeeper Mads Hermansen.
Victory took Chelsea, who drew their opening game 0-0 against Crystal Palace, top of the Premier League for the first time since December 2021.
Chelsea had been dealt a blow before kick-off as Cole Palmer left the field during the warm-up and was pulled out of Enzo Maresca’s line-up as a precaution due to a muscle injury.
“The last four or five days he was not 100 percent. We prefer not to take any risks and we see in the next hours [how serious the injury is],” said Maresca.
Palmer’s withdrawal opened the door for Brazilian wonder kid Estevao to show his potential on his first Premier League start.
Pedro made himself an instant hero for the Blues by scoring three goals in as many games as Chelsea won the Club World Cup less than six weeks ago.
The former Brighton forward had a simple task for his first Premier League goal for the club as he headed in Marc Cucurella’s flick-on from a corner.
West Ham briefly thought they had retaken the lead through Niclas Fuellkrug until the goal was disallowed for offside after a VAR review.
Moments later, the hosts trailed when Pedro picked out Neto to finish at the far post.
Estevao scored against Chelsea in his final game for Palmeiras at the Club World Cup and has been hailed as one of the brightest young talents in world football.
The 18-year-old showed his explosive pace to burst clear of the sluggish West Ham defence and square for Fernandez to make it 3-1 on 34 minutes.
One of West Ham’s few new arrivals, goalkeeper Hermansen, was at fault for Chelsea’s fourth and fifth, dropping a corner ball at the feet of Caicedo for him to prod into an empty net and getting nowhere near the Blues’ next corner to allow Chalobah to rub salt into the Hammers; wounds. (AFP)