After a goalless draw at Selhurst Park 13 days previously, Gomes’ inch-perfect set piece in front of the Sir Philip Carter Park Stand just before half-time settled it at Goodison Park.
Sean Dyche made four changes from the side that started the home draw with Aston Villa, with Joao Virginia – who impressively kept a clean sheet in the initial Cup clash with Palace, Nathan Patterson, Dwight McNeil and Gomes recalled to the starting line-up.
Abdoulaye Doucoure and Seamus Coleman missed out on the matchday squad, while Jordan Pickford and Arnaut Danjuma took a place on the bench.
With the temperature dropping below freezing, the contest – in front of a sell-out Goodison crowd – took a while to warm up, in truth.
Dominic Calvert-Lewin dug out a shot from an acute angle on 13 minutes, forcing Sam Johnstone into action as he clawed the ball behind for a corner.
The first real flash point came midway through the first half when Jack Harrison went down under a challenge from Tyrick Mitchell on the line of Crystal Palace’s penalty area – but the Blues’ appeals for a penalty were waved away by referee Tony Harrington were waved away and the wait for a first spot-kick of the season went on.
Virginia was then called into action for the first time of the night, holding on well to Eberechi Eze’s low, side-footed drive at the end of a rare free-flowing move from the visitors.
The deadlock was broken three minutes before the half-time interval – and it was Gomes, on only his second start of the campaign, who was at the centre of it.
A fortunate ricochet into the Portuguese midfielder’s path looked to have released him through on goal, only for Jefferson Lerma’s desperate sliding challenge from behind to stop him in his tracks.
The Palace midfielder was booked, before Gomes dusted himself down to curl in a stunning curling effort into the back of the net via the inside of the post, leaving a sprawling Johnstone with no chance.
It was Everton’s first goal direct from a free-kick for 196 games, the last scored by Lucas Digne in a Carabao Cup second round win at Lincoln City in August 2019.
Palace went close to an immediate response but Virginia pulled off an excellent one-handed save to keep out Mitchell’s arrowed drive – which was bound for the top corner – following a slide-rule pass from Eze.
Roy Hodgson made a triple substitution just after the hour and one of those changes – Naouirou Ahamada – threatened moments after being introduced, pinching possession on the halfway line before bursting down the right channel and picking out Odsonne Edouard with a low cross. Fortunately for the Toffees, Virginia was on hand again to keep out the Frenchman’s effort with his feet.
The visitors made a double 10 minutes later in a bid to force their way back into the tie, but Dyche’s Blues continued to control proceedings with relative comfort, even if clear opportunities continued to evade both sides.
As the game reached the closing quarter of an hour, Onana’s incisive pass to Calvert-Lewin led to a snap-shot that fizzed just the wrong side of the post with Johnstone diving at full stretch.
There was time for two more chances in stoppage time – one at either end but on both occasions the goalkeepers came out on top.
First, the Eagles broke down the left and Marc Guehi’s inviting cross was met with a firm header by Jeffrey Schlupp that required another intervention from Virginia.
Then, as a direct response, McNeil and substitute Lewis Dobbin led a quick breakaway – the latter forcing Johnstone into a save from point-blank range inside the six-yard box.
That would be the last action of this mammoth 120-minute-plus battle, with Everton now set to face Luton Town on home soil on Saturday 27 January(3pm GMT kickoff). Ticket information will be available on evertonfc.com on Thursday.
