Everton needed an extra-time winner from Abdoulaye Doucoure to finally see off Championship side Rotherham and reach round four of the FA Cup.
The Premier League side – featuring the likes of James Rodriguez and Lucas Digne – led through Cenk Tosun.
But Rotherham forced saves from Robin Olsen before Matthew Olosunde hooked in a deserved equaliser after the break.
A VAR call denied Tosun a second at the death but substitute Doucoure steered home a winner early in extra time.
It was tough on Rotherham, who would have earned a replay after it was level at the end of normal time were it not for the need for FA Cup ties to be resolved in one match this year – meaning no replays – as a result of Covid-19’s impact on the football calendar.
On another day, a passive Everton display over the 90 minutes might have been enough to edge through such a tie but Rotherham clearly fancied the chance to reach round four for the first time in 18 years and inject some joy into a tough season battling Championship relegation.
After Tosun’s clever chipped finish – his first Everton goal since 2019 – Paul Warne’s side rallied, with Olosunde and Daniel Barlaser seeing shots saved, while Matt Crooks glanced a header over.
When Olosunde did level after the break, Everton manager Carlo Ancelotti’s decision to not name top-scorer Dominic Calvert-Lewin or Brazilian forward Richarlison on the bench made the home side appear slightly vulnerable.
But he did introduce Bernard and Doucoure, who slotted into the bottom corner to keep Everton’s hopes of landing a first major trophy since 1995 alive.
‘Everton’s tough day’ – reaction
Everton assistant manager Duncan Ferguson: “It was a tough match so you are always fearing the worst when they got a corner in the last minute, so it was a wee bit of relief.
“We started well and Cenk took his goal well. It was a tough game for us and one we were delighted to get through.”
Rotherham manager Paul Warne: “I thought we took the game to them after we conceded and I thought we were the better side in the first half.
“We could have got a 2-1 in and no-one would have complained about it.”
Everton travel to Wolves on Tuesday while Rotherham have a week until they go to Derby on 16 January.