Match ends, Everton 0, West Ham United 1.
West Ham manager David Moyes said winning at Everton for the first time since he left the club was "special".
Tomas Soucek's late goal gave West Ham a 1-0 Premier League victory at Goodison Park.
"Always going back to your old clubs is special," said Moyes, who had lost on his previous four visits to Everton following his departure in 2013 after 11 years in charge.
"I had a brilliant time here - great years - but I want to do it again at West Ham and that means going and winning at the other clubs."
Aaron Cresswell's shot deflected off Everton defender Yerry Mina into the path of Soucek, who tapped home in the 85th minute of a largely uneventful game.
Everton, who had won their previous four league games, missed out on climbing to second in the table.
Soucek strikes after defences dominate
To say the first 85 minutes lacked creativity would be an understatement. Neither side were able to dominate going forward, with the first shot on target coming on the stroke of half-time.
Moyes and Everton manager Carlo Ancelotti have built their teams around defensive stability.
Soucek's goal was only the second Everton have conceded in five league games, while West Ham have now kept two consecutive clean sheets.
"Coming here tonight and winning was really important," Moyes said.
"Everton are in a great moment, have been playing well, getting great results and had a chance to go second, so you couldn't underestimate what it would mean to Everton. And we were on the back of our third game in six days."
West Ham had the pick of the chances, Cresswell forcing Jordan Pickford into a smart save and Michail Antonio having a drilled effort kept out in the second half.
They also proved difficult to break down and were playing the better football when midfielder Soucek, their leading scorer this season, netted his fifth goal of the campaign.
West Ham win despite absentees
Although West Ham picked up a third away victory in five games, there were areas of concern for Moyes.
Right-back Ryan Fredericks dropped out of the squad after testing positive for Covid-19, while goalkeeper Lukasz Fabianski was injured during the warm-up.
"Ryan is fine," said Moyes. "We are going to make sure we give the players four days off so they can have some time and we make sure we shut the training ground down for a few days because it is very bad, Covid, at the moment.
"The only reason is so we can get another clean and keep people out."
Back-up keeper Randolph was rarely tested by Everton, who brought on Colombia forward James Rodriguez in the second half for his first appearance since 5 December.
Everton remain fourth in the table, while West Ham stay 10th.
We must keep our belief high - Ancelotti
Everton manager Carlo Ancelotti told BBC Sport: "The game was in the balance. We didn't have a lot of opportunities; they didn't have a lot of opportunities.
"We have to accept the result. It will be important to keep our belief high.
"We are more comfortable defending and using the counter-attack. When we have the ball we have more difficulties and we have to adjust this.
"We are in the position we would like to be and hopefully we can be there at the end of the season. That is our target."
Everton stutter at home - the stats
- Everton have lost three of their past five Premier League home games, as many defeats as they suffered in their previous 19.
- Everton boss Carlo Ancelotti has faced David Moyes more times in the Premier League without winning than against any other manager, drawing three and losing three of their six meetings.
- Aaron Cresswell made his 200th Premier League start for West Ham, only the second Hammers player to reach that figure after Mark Noble (365).
- West Ham's Jarrod Bowen has been substituted 15 times in the league this season from 16 starts, more than any other player.
- Everton striker Dominic Calvert-Lewin is without a goal in five league appearances after netting 11 in his previous 11 games.
Everton take on Championship side Rotherham in the FA Cup third round on 9 January, while West Ham travel to National League side Stockport County on 11 January.
- 22GodfreyBooked at 59mins
- 26DaviesBooked at 77mins
- 10G SigurdssonSubstituted forAndré Gomesat 65'minutes
- 20BernardSubstituted forRodríguezat 64'minutes
- 9Calvert-LewinSubstituted forTosunat 79'minutes
- 21André Gomes
- 20BowenSubstituted forYarmolenkoat 73'minutes
- 18FornalsSubstituted forLanziniat 73'minutes
- 22HallerSubstituted forAntonioat 59'minutes
- Kevin Friend
- Shots on Target
Second Half ends, Everton 0, West Ham United 1.
Attempt missed. Manuel Lanzini (West Ham United) left footed shot from a difficult angle on the left is just a bit too high. Assisted by Michail Antonio.
Foul by James Rodríguez (Everton).
Saïd Benrahma (West Ham United) wins a free kick in the defensive half.
Goal! Everton 0, West Ham United 1. Tomas Soucek (West Ham United) right footed shot from the centre of the box to the centre of the goal.
Attempt missed. Aaron Cresswell (West Ham United) left footed shot from outside the box misses to the right.
Attempt saved. Tomas Soucek (West Ham United) right footed shot from the centre of the box is saved in the centre of the goal. Assisted by Andriy Yarmolenko.
Foul by Richarlison (Everton).
Angelo Ogbonna (West Ham United) wins a free kick in the defensive half.
Attempt missed. Yerry Mina (Everton) header from the centre of the box misses to the left. Assisted by Mason Holgate with a headed pass following a set piece situation.
Richarlison (Everton) wins a free kick on the left wing.
Foul by Tomas Soucek (West Ham United).
Substitution, Everton. Cenk Tosun replaces Dominic Calvert-Lewin.
Foul by André Gomes (Everton).
Tomas Soucek (West Ham United) wins a free kick in the defensive half.
Tom Davies (Everton) is shown the yellow card for a bad foul.
Foul by Tom Davies (Everton).
Michail Antonio (West Ham United) wins a free kick on the left wing.
Foul by Tom Davies (Everton).
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