With the temperature sub-zero the match did little to animate the 37,796 hardy souls in attendance but Gomes’ strike – the Toffees’ first from a direct free-kick in 197 games in a run dating back to August 2019 – was the one real highlight.
Gomes’ long stretch without a goal on home soil went back even further than Lucas Digne’s set-piece against Lincoln in the Carabao Cup in August 2019 but it was worth the wait.
Initially fouled by Jeffrey Schlupp 25 yards out the Portuguese took responsibility and curled a sumptuous effort over the wall and in off the post.
After three matches without a goal it was very much worthy of securing Everton a first third-round victory over top-flight opposition since they beat Sheffield Wednesday in 1988.
Palace’s winter break meant they had a free fortnight from the original tie – itself a drab goalless draw – to prepare. Everton, whose own break was eaten into by this replay, had three days.
Manager Sean Dyche made four changes from Sunday’s goalless draw with Aston Villa but two were enforced – Seamus Coleman and Abdoulaye Doucoure were both carrying knocks – while he rested goalkeeper Jordan Pickford.
His deputy Joao Virginia had arguably his best game in his five-year spell at the club with a string of good saves to keep a clean sheet.
Gomes was deployed in Doucoure’s position just behind the striker, bringing a more measured, less energetic approach which meant Dominic Calvert-Lewin was often left isolated.
The England striker, now more than 17 hours without a goal, had a chance early on but his near-post shot was turned behind by Sam Johnstone before watching a promising Jack Harrison cross float over his head.
Quality of the final ball was a frequent cause for consternation as it was almost always over-hit and that left Calvert-Lewin frequently chasing lost causes down the channels.
Palace, by contrast, had much better control in the final third and in Eberechi Eze a player whose direct running opened up opportunities, highlighted by him side-stepping Vitalii Mykolenko only to fail to properly test Virginia, while Schlupp flicked over a pass from Jefferson Lerma.
But Schlupp was to have a more pivotal role at the other end with his unnecessary bringing down of Gomes as he set off on a lone run towards the penalty area allowing the Portuguese to exact immediate revenge.
Virginia made a good save from Tyrick Mitchell to ensure their half-time lead and will have been delighted to see Eze was surprisingly taken off in the 65th minute, prompting chants to boss Roy Hodgson of “You don’t know what you’re doing” from the away fans.
However, they were almost proved wrong when Odsonne Edouard’s shot on the turn was well saved by Virginia.
Calvert-Lewin’s almost three-month wait for a goal continued when he flashed an angled shot across goal while Gomes’ replacement Lewis Dobbin had a header deflected wide.
But the final say went to Virginia who made two crucial saves in added time to secure a home tie against fellow Premier League strugglers Luton.