Reports ahead of the match, between two sides entering the weekend in the relegation zone, suggested the Hammers boss would lose his job should his side be beaten, but instead it was Frank Lampard leaving the London Stadium fearing for his position.
Jarrod Bowen netted twice from close-range in the first half to put the hosts in control and it was an advantage they kept hold of after the break, ending their seven-match winless run in the League.
Danny Ings was named on the bench after completing his move to West Ham, and he wouldn’t have been particularly impressed with what he saw in the opening half an hour.
His new team-mates showed very little ambition, though Everton were no great shakes themselves on a pitch full of players lacking in confidence.
West Ham eventually put together a good ten-minute spell and it was enough for them to take complete control. Bowen opened the scoring as the ball fell for him from a corner, and the winger soon had his second as Michail Antonio broke quickly and pulled the ball back for him.
Alex Iwobi had a massive chance to halve the deficit just before the break, his effort flicking off the outside of the post, as the mood in the away end continued to darken.
Everton pinned West Ham back for much of the second-half, though failed to turn that pressure into clear-cut chances. Emerson Palmieri nearly put the match to bed on the counter, Jordan Pickford doing well to tip his strike onto the bar.
Ings came on for the final 20 minutes to make his West Ham bow. He had very little involvement but that was of little concern for the home fans, who watched their side keep Everton at bay and pick up a massive three points.