Andriy Yarmolenko’s strike a minute from time ultimately provided a huge lift to the Hammers’ survival hopes.
Yet West Ham thought they had taken the lead midway through the first half when Tomas Soucek bundled home from a corner.
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But VAR took almost four minutes to decide that Michail Antonio, lying on the ground as Soucek lifted the ball over him, was marginally offside and in the line of vision of Chelsea keeper Kepa Arrizabalaga.
“I was spewing, I was thinking are we ever going to get a decision here?” Moyes said.
“I don’t want to whinge at the decisions but everybody seems to tell me it should have been a goal.
“Some of the things that have gone against West Ham recently have been really poor.
“I was fired up at the sense of injustice – I was angry at the time. But the boys never let it affect us.
“I have to say that the boys didn’t let it affect them. We wanted them to play better in the second half than they did in the first and we thought we could do as well and they did.
“Some of the things that have gone against West Ham recently have been really poor but I told the players we had to change our luck.
“I think it was a good performance. The players worked really hard and deserve a huge amount of credit.”
Moyes, already angry, was ready to explode moments later when Issa Diop tripped Christian Pulicic and Willian scored from the penalty spot.
However Soucek, the unlucky scorer of an own goal against Spurs after VAR failed to spot a handball, finally saw things go his way in first-half stoppage time,when he headed in another corner.
Antonio put West Ham ahead after the break, before Willian struck again with a stunning free-kick, but Yarmolenko settled it to put some much-needed daylight between the Hammers and the relegation zone.
Defeat meant Chelsea missed the chance to climb above Leicester into third, and manager Frank Lampard said: “I think it’s something which has happened this season.
“We have a lot of hard work to do to get to where we want to be. We have to work towards consistency. We have Watford at the weekend and we have to carry on.
“I don’t feel let down by the defenders. We had mistakes by all the players which cost us the game.
“When a team is bigger than you as they were today, then you can work on it as much as you want but they can out-jump you. The players have to deal with that on the pitch.
“I wouldn’t call it a wake-up call because every game is different. It can happen. It’s something we knew. We have to move on.”