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 the UK government's lockdown and impact on the football calendar.