Before kick-off, there was a minute’s applause for Matt Beard, who managed both clubs and passed away last Saturday.
West Ham manager Skinner and Paul Green, head of women’s football at Chelsea, jointly laid a wreath in the centre circle to pay their respects.
The hosts made a bright start with striker Viviane Asseyi sending an effort wide, before another shot dribbled just past the post.
Two minutes later, ruthless Chelsea were ahead and there was no turning back.
West Ham’s defensive woes were summed up by midfielder Riko Ueki’s loose pass back towards goal which was pounced on by Cuthbert for the visitors’ third goal.
And Skinner’s side contributed to their own downfall.
Belloumou’s red card for pulling Thompson’s hair was a flashback to an incident that occurred in the quarter-finals of the Euros with Germany’s Kathrin Hendrich sent off for doing similar to France centre-back Griedge Mbock in the box.
It just made West Ham’s task even harder and their only chance of a consolation was when Ffion Morgan – making her first start for the Hammers – went clean through, but her finish was blocked by the legs of Chelsea goalkeeper Hampton.
But seconds later, the Blues scored their fourth through Kaptein.
The Hammers have now conceded four or more goals in three successive WSL games for the first time ever. In addition, they have lost six consecutive in the league, the worst record in the club’s history.
Things need to improve quickly if they are to pick up points and avoid a relegation battle.