Edinson Cavani and Anthony Martial struck late goals as Manchester United claimed a scrappy 2-0 victory over Everton at a bitterly cold Goodison Park on Wednesday to set up a League Cup semi-final with rivals Manchester City.

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United wasted numerous opportunities in the opening stages and at times the play was dire from both sides as the game appeared to be heading for penalties before Cavani collected the ball on the right wing, skipped inside onto his left foot and fired past Everton goalkeeper Robin Olsen.

Martial added a second with virtually the last kick of the game as the visitors now meet City for a place in the April 25 final, while Championship side Brentford take on Tottenham Hotspur in the other last-four clash.

"It was an excellent performance and we should have been out of sight, we had three or four great chances. We need to be more clinical," United captain Harry Maguire told Sky Sports

"We are expected to win trophies. It's important to reach these big games but we have to start winning them and lift some trophies for this club.

Everton will feel aggrieved that the influential Cavani was still on the pitch after receiving only a verbal warning from referee Bobby Madley when he shoved Yerry Mina to the ground with his hands close to the Everton defender's throat in an off-the-ball incident in the first half.

But with the Video Assistant Referee (VAR) absent in this competition until the semifinal stage, there was no further action taken when replays showed Cavani was lucky to escape sanction.

His quality proved the difference in opening up the tight Everton defence though, with Martial's insurance goal coming in the dying seconds as the home side pushed bodies forward in search of an equaliser.

United keep up their excellent record away from Old Trafford and are now unbeaten in 20 domestic games in all competitions, winning 18 of those.

The visitors dominated the early exchanges and put Everton under pressure with a succession of chances that were wasted, Cavani coming close twice.

Everton finally woke from their slumber as, roared on by 2,000 fans in Goodison Park, Dominic Calvert-Lewin and Gylfi Sigurdsson both had efforts on goal that needed saving by United keeper Dean Henderson.

The second half had little of the spark of the first, both sides misplacing passes in the attacking third and neither keeper having a serious save to make until Olsen was picking the ball out of his net for Cavani's opener.

Everton manager Carlo Ancelotti was disappointed that his side couldn't get the favourable result.

"We did enough to win -- good performance we needed to defend which we did well but more in the second half," he said. "We had a difficult start but after 20 minutes the game was under control -- we didn't play enough attacking football but we had to defend and until the last 20 minutes we did that well."