After back-to-back losses to Arsenal and Istanbul Basaksehir, Sunday's (AEDT) Premier League clash at Goodison Park was viewed by some as a must-win match for Solskjaer amid increasing speculation over his future.

Things looked worrying for the Red Devils boss when Bernard put Carlo Ancelotti's side ahead, but Fernandes scored twice before half-time and Cavani struck at the death to deliver three valuable points.

Anthony Martial, back from a three-game domestic suspension, dragged a shot wide from a promising position as United sought a positive start.

The visitors were behind 19 minutes in, though, as Bernard squeezed an effort into the bottom-left corner through Aaron Wan-Bissaka's legs after Dominic Calvert-Lewin had helped on Jordan Pickford's long kick.

Fernandes equalised in the previous meeting at this ground and he drew United level again, powering a header beyond Pickford after running into the box to meet Luke Shaw's delivery.

The Portugal international then put his side ahead, his cross at the end of a 20-pass sequence going in off the right-hand post after Marcus Rashford had tried to glance it in.

United captain Harry Maguire wanted a penalty when Pickford and Michael Keane clashed with him after the Everton goalkeeper had dropped the ball, but neither the officials on the pitch nor those using VAR (video assistant referee) agreed.

Rashford smashed another strike at Pickford as United failed to find a third goal on the break, although it kept the home side at bay despite the Toffees controlling possession in the second half.

As Everton poured forward in stoppage-time, Maguire's interception sent Fernandes away on the break, and he waited before teeing up Cavani to sweep home.

Defeat here was highly unlikely to spell an immediate end to Solskjaer's time in charge, but this was an important result to quieten some of the recent mounting criticism.

The fact it came against a side unbeaten in three games against United, at a ground where it lost 4-0 in April last year in its worst display under the Norwegian, made this performance more impressive.

United is on 10 points from seven matches and three behind Everton, whose manager has now suffered three consecutive league defeats for the first time since November 2006, when he was at AC Milan.

United hosts West Bromwich Albion after the international break on 22 November (AEDT). On the same day, Everton will travel to Fulham.