Carlo Ancelotti went strong, with just four changes from the weekend win at Crystal Palace, including starts for Allan and James Rodriguez. Niels Nkounkou also returned after impressing in the previous two rounds.
They started strongly too, maintaining the momentum from the weekend. Michael Keane’s long pass over the top was controlled by the onrushing Calvert-Lewin, who lobbed Darren Randolph to put the Toffees ahead with his sixth goal of the campaign after 11 minutes.
Richarlison could have doubled the lead when he jinked into the area, but his stabbed finish was superbly pushed over the top by Randolph.
The Brazilian had the ball in the net moments later after running onto James’ delicious pass, but he was denied by the offside flag.
The was yet another defensive injury blow shortly before the break when Kenny went over on his ankle and had to come off. Seamus Coleman was able to take his place, but Everton’s defensive stocks are looking perilously thin. Incomings needed before Monday’s deadline methinks.
West Ham had offered little as an attacking force though they went close before half-time when Manuel Lanzini headed just wide from eight yards.
Everton were more than worthy of their lead at the break, but paid the price just 26 seconds into the restart when Robert Snodgrass curled a wonderful effort into the corner from the edge of the area.
Everton weren’t deterred and the Blue wave continued to pour forward, with Richarlison hitting the post from a tight angle. Sigurdsson then saw his shot well saved by Randolph, who was having an inspired evening.
He could do little with Richarlison’s effort minutes later, though, with his shot from distance taking a wicked deflection off Declan Rice and beyond the wrong-footed goalkeeper.
That was all the luck Richarlison would have as he rolled his ankle minutes later and had to come off - another worrying injury to a key player. Fingers crossed it is not too serious.
Lanzini shot wide from Yarmolenko’s knockdown before the remarkable injury hat-trick was completed by Allan, who looked to have injured his groin and couldn’t continue.
Allan’s injury looked the worst of the three, as he appeared to indicated a pull or tear, any lengthy absence would be a huge blow given the crucial role he plays in midfield.
Haller’s downward volley pushed over by Pickford as Everton began to drop deep and putt the supporters through the mill.
Thankfully, Everton put the game to bed minutes later.
Alex Iwobi’s curling shot from just inside the area thumped off the inside of the post but Calvert-Lewin was alert to bury the rebound with a first-time, close-range finish.
Calvert-Lewin, who must surely earn an England call-up this week, completed his second hat-trick of the campaign when he ran onto Gylfi Sigurdsson’s pass and calmly stroked the ball beyond Randolph for his eighth goal of the campaign already.
It is yet another wonderful win, 20 goals in six games now, and moves the Toffees to within two games of Wembley.
But those three injuries will be of huge concern, not just for Brighton on Saturday but the looming Merseyside derby in a fortnight’s time.
That, though, is for another day. Now we should just enjoy an Everton side that is not just winning, but winning with style.
Let’s see where that takes us.