Antonio Rudiger's header and Willian's stunning stoppage-time strike secured Chelsea a place in the EFL Cup quarter-finals as David Unsworth's first game in temporary charge of Everton ended in a 2-1 defeat.

Ronald Koeman's 16-month stint in charge of Everton was brought to a halt on Monday, following a humiliating 5-2 home defeat to Arsenal that left them 18th in Premier League.

However, a rejuvenated second-half display showed Everton's quality - with a moment of magic from Willian in the 92nd minute ensuring that Dominic Calvert-Lewin's effort soon after was a mere consolation.

Rudiger's superb 26th-minute effort, the defender's first goal for the Premier League champions, looked to have taken the spirit out of the Toffees, but Unsworth's side responded superbly and dominated in the second half - Willy Caballero pulling off a string of saves to preserve Chelsea's lead.

Ademola Lookman went close with a blistering strike against the bar just before Chelsea wrapped up the win late on deserved.

Ultimately, though, it is now just two wins in 14 matches across all competitions for managerless Everton, who face fellow strugglers Leicester City next time out.