A late goal from Tomas Soucek gave West Ham United a 1-0 win at Everton in the first Premier League game of 2021 that had been short on fireworks until the Czech midfielder's well-deserved winner in the 86th minute.
West Ham wasted some decent chances until Soucek struck late, first forcing Jordan Pickford to parry a shot before reacting quickest to steer home Aaron Cresswell's deflected effort for the winner.
The victory leaves West Ham 10th in the standings with 26 points while Everton, who could have gone second with a win, remain in fourth spot on 29 points.
It took until just before halftime for either side to register a shot on target as Everton's Brazilian winger Bernard fired a fizzing drive goalwards, but Randolph was alert to the danger and got down smartly to keep the ball out.
The introduction of Mikhail Antonio as a 59th-minute substitute provided a much-needed shot in the arm for West Ham and they had a flurry of chances in quick succession around the hour mark, but it was Soucek's late strike that sealed it.
Cresswell got plenty of power on his shot, which got a heavy deflection before falling perfectly for Soucek to stab it home from close range.
Soucek's goal gave West Ham boss David Moyes his first victory at Goodison Park since leaving Everton in 2013.
"To come to Goodison Park and get three points and to play as well as we did ... we got the reward for it," a delighted Moyes told BT Sport.
"It was important to get something from this. It was our third game in six days, we asked the players to do it and they did a brilliant job."
Everton boss Carlo Ancelotti was disappointed not to get more out of the game.
"The game was in the balance. We didn't have a lot of opportunities, they didn't have a lot of opportunities," he told BBC Sport.
"We have to accept the result. It will be important to keep our belief high ... 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."