Calvert-Lewin's double and a strike from Oumar Niasse was enough to overcome Championship strugglers Sunderland

Calvert-Lewin netted a brace at Goodison Park in the Carabao Cup. Credit: PA

Dominic Calvert-Lewin netted a brace and Oumar Niasse also got on the scoresheet as Everton's miserable run came to an end with a 3-0 Carabao Cup third-round victory over Championship strugglers Sunderland at Goodison Park.

Calvert-Lewin produced the Toffees' first goal since August 24 with a cool finish in the 38th minute before adding another composed strike six minutes after the break.

The England Under-21 forward was subsequently denied a superb hat-trick as his header came back off the post, before substitute Niasse marked his first Everton first-team appearance since May 2016 by registering his maiden goal for the club with seven minutes to go.

Everton went into the tie in major need of a boost having lost each of their previous four games, conceding 12 goals along the way and scoring none.

They were not entirely convincing while stopping the rot here, surviving a few scares as their former player James Vaughan passed up chances.

But Everton fans will certainly be glad to have had a few things to cheer about here, particularly with Calvert-Lewin showing his predatory instincts after a period in which the club's failure to really replace Romelu Lukaku, despite the considerable spend of the summer, has appeared glaring.

There was also plenty of appreciation for Niasse's contribution as the Senegal forward returned in style following his time being frozen out.

Oumar Niasse gave plenty for Ronald Koeman to think about with his performance. Credit: PA

Boss Ronald Koeman made eight changes to his starting XI from Sunday's 4-0 defeat at Manchester United, with Wayne Rooney, two days on from pleading guilty to drink driving, and ex-Sunderland goalkeeper Jordan Pickford among the players watching from the stands having been left out of the 18.

Koeman's opposite number Simon Grayson, whose side are 21st in the Championship, named a line-up featuring six changes, and three ex-Everton players in Vaughan, Jack Rodwell and Darron Gibson.

With both sides' shirts displaying the Bradley Lowery Foundation logo ahead of being signed and auctioned to raise funds for the charity, it was Sunderland who had the first real opportunity of the contest, Vaughan shooting wide from the edge of the box in the fifth minute after Muhamed Besic lost possession.

The hosts started to exert some pressure thereafter, with Nikola Vlasic firing a volley into the side-netting, Calvert-Lewin striking wide and Sandro Ramirez having a free-kick saved by Jason Steele.

Former Everton forward Vaughan challenges Williams. Credit: PA

Vlasic subsequently cracked another shot narrowly off-target, but in truth, Everton looked as if they were struggling to find much rhythm until Calvert-Lewin broke the deadlock with seven minutes of the first half left.

The ball was worked from Vlasic, via Davy Klaassen, to Calvert-Lewin, who showed nice footwork as he kept his composure in the box amid a clutch of Sunderland players to slot past Steele.

The former Sheffield United man then doubled the advantage shortly after the break when he collected Sandro's through-ball and struck confidently into the net.

Sunderland might have pulled a goal back but Vaughan missed the target twice with headers, either side of substitute Ademola Lookman being denied by a fine Steele double save.

Niasse, who had come on for Calvert-Lewin, then sealed Everton's fourth-round spot with a flicked finish, having been set up by Tom Davies.