The miserable denouement to David Moyes’s time at West Ham stands in stark contrast to ­Mauricio ­Pochettino’s increasing joyfulness on the other side of the capital. European football is on the cards after Chelsea cruised through their second ­London derby in the space of three days and, for all the doubts hanging over Pochettino’s future, it would surely go down as an act of extraordinary self-sabotage if the Argentinian’s bosses make a change this summer.

The main takeaway from this 5-0 win over a supine West Ham is that something is beginning to stir at Stamford Bridge. Instead of ­crumbling after last month’s 5-0 defeat to Arsenal, Chelsea have responded by dominating Aston Villa, Tottenham and West Ham. Far from shrinking, these young ­players are starting to grow and mature. Above all, they are starting to ­resemble a proper team and, after a season so full of turbulence, the wisest thing that Chelsea’s owners can do now is accept that Pochettino is the man to bring coherence to their £1bn project.

“It is a process that takes time,” Chelsea’s head coach said. “You never know if it will be one month, six months or a year. But they are starting to live like a group of ­players with links. I am so pleased with that, helping them to grow and be mature. It is only the first step, but a massive step.”

Chelsea, who are two points below sixth-placed Newcastle, were in a vibrant mood after beating Spurs on Thursday. Moisés Caicedo, who is starting to justify his £115m fee, excelled in midfield. Marc Cucurella continued his unlikely ­resurgence as an inverted left-back. The ­awkward, powerful Nicolas Jackson ­immediately had joy against West Ham’s painfully immobile back four.

West Ham have completely forgotten how to defend. It is damning for a manager as pragmatic as Moyes that his side, with 70 goals conceded this season, have the worst record outside the bottom three.

Afterwards Moyes would talk about a lack of “mental toughness” and ­suggest that the ­leakiness is down to selling Declan Rice last ­summer, but the harsh reality is the Scot’s methods are no longer working. West Ham have become an easy team to play. Tomas Soucek and Edson ­Álvarez, who went off at half-time, have not provided enough protection in midfield. Kurt Zouma and Angelo Ogbonna toiled in ­central defence. Emerson Palmieri, the ­former ­Chelsea left-back, was given a torrid time by Noni Madueke.

There would be well-deserved boos from the away end at half-time. Cole Palmer sparked the rout in the 15th minute, his 21st league goal of the season an inevitability when Zouma failed to deal with Madueke’s cross. Palmer had time to pick his spot and he made it look easy, lashing a rising shot past Alphonse Areola.

Their resistance broken, West Ham at least threatened an instant ­equaliser, Jarrod Bowen heading against the bar. Wary of Chelsea’s habit of slipping into doziness, Pochettino urged them to wake up. Madueke threatened from 20 yards and Trevoh Chalobah wasted an easy header from a corner.

West Ham folded, Lucas Paquetá an indolent disgrace in midfield, too many players refusing to track back. It looked like they had given up on their season. It is no secret that change is coming. Julen Lopetegui is the ­frontrunner to replace Moyes, whose ­contract is up. There have been talks with Sporting’s Rúben Amorim. Moyes’s power has been diminished.

Chelsea, by contrast, are playing for their manager. Displaying the intensity that characterises a Pochettino team in full flow, they led 2-0 when Zouma’s attempt to cut out Palmer’s pass sent the ball spinning to Conor Gallagher, who charged in to spank a brutal volley past Areola.

Another thrashing beckoned. West Ham, whose slim hopes of European qualification are over after one win in nine league games, have lost 6-0 to Arsenal, 4-1 to Aston Villa and 5-0 to Fulham this season. In their previous away game, they were 4-0 down to Crystal Palace after 31 minutes. Perhaps only trailing Chelsea 2-0 after 30 minutes was progress.

Or not. Thirty-six minutes in, Mykhailo Mudryk delivered a ­corner to the far post and the unmarked ­Thiago Silva headed the ball across for Madueke to score from close range.

The action became carefree. Palmer evaded Álvarez and crossed for Gallagher, who hit the bar from three yards out. Bowen, the sole source of defiance, sent two more efforts against the woodwork. Chelsea had their fourth early in the second half, Madueke running clear and unselfishly squaring to Jackson, who tapped into the empty net.

Chelsea strolled through the rest of the game. Christopher Nkunku boosted the good vibes by coming on for his first appearance since ­February. Jackson added the fifth, finishing crisply from Caicedo’s pass. Moyes stayed on the bench, a picture of gloom.