The Red Devils booked their place in the Carabao Cup semi-finals with the victory over the Toffees, where they will meet local rivals Manchester City in January.
Cavani produced a crisp finish to break the deadlock late on, opening the scoring in the 88th minute, before Anthony Martial struck on the counter-attack to secure the win in the final minute.
The Uruguayan had missed some good chances in the first half, with Robin Olsen making a couple of good saves and when asked about Cavani’s goals, it was his missed chances that Solskjaer remembered.
‘Not bad. Which one though? Maybe he should’ve scored the three in the first half!’ Solskjaer joked.
‘No, he’s a top striker. Movement, quality, and of course the left foot strike was excellent.’
Cavani was involved in a controversial moment, though, as he appeared to grab Everton defender Yerry Mina by the throat and shove him to the floor.
There was no VAR in the game, but the striker would have undoubtedly been shown a red card if there had been.
However, Solskjaer dismissed the incident, saying it was just a bit of South American passion in a physical contest.
‘This was a proper game of football. With fans, with some tackles, with some yellow cards, some chances at both ends. I enjoyed it.’
United take on City for a place in the final, with Tottenham facing Brentford in the other semi-final.