Edinson Cavani who possibly should not have been on the pitch, finessed a left-footed strike into the bottom-left corner to snatch victory.
Anthony Martial then secured the win for United in added time and prevented any last minute antics from the Toffees.
United were dominant in the first half but failed to take their chances but Everton failed to mount any clear-cut chances.
Story of the game
Ole Gunnar Solskjaer seemed to have addressed United's issue of starting games slowly as they opened the first ten minutes with four corners and should have gone one or two goals up.
Robin Olsen, who took Jordan Pickford's position on the night, denied Cavani with a superb double save.
Mason Greenwood then came closest to giving United the lead on the 25 minute mark. Alex Telles whipped in a cross for Greenwood to glance a header goalwards, but the 19-year-old's header struck the post.
Dean Henderson was forced into making a terrific save from a Gylfi Sigurdsson free-kick. The Icelandic international's strike was heading for Henderson's top-right corner. If it were to have gone in, Everton would have taken a very undeserved lead as they were nervous and defensively shaky.
Despite such a promising start for United, they went down the tunnel at half-time level. For Carlo Ancelotti's side, he would have been extremely thankful to get to the break all-square.
United started the second half similarly to the first as Cavani hit the side-netting early on. Cavani would then count himself lucky to remain on the pitch after an apparent 'chokeslam' on Yerry Mina.
Dominic Calvert-Lewin was nearly gifted an opportunity to steal the win after he picked up Harry Maguire's loose pass in the middle of the park. Eric Bailly tracked back and managed to clear the danger.
Cavani finally got his goal in the 87th minute to give his side the lead. It was an excellent finish from the Uruguayan striker.
Substitute, Anthony Martial then confirmed the victory with a composed finish in stoppage time.
What does this mean for both sides' trophy cabinet?
The Toffees continue their search for silverware as they are 25 years without with a trophy. Their only chance to win a trophy this season will come in the FA Cup when they face Rotherham in January. Everton still have never won a league cup.
United under Solskjaer remain trophyless but are into their fourth semi-final, their last trophy came under Jose Mourinho's reign when they won the Europa League in 2017. The draw for the semi-finals will take place later this evening.