Cavani scored for United in the 88th minute of the Carabao Cup quarter-final tie against Premier League rivals Everton away from home at Goodison Park.
The former Napoli and Paris Saint-Germain striker found the back of the net with a wonderful curling effort from 20 yards.
Anthony Martial doubled the advantage for the Red Devils in the sixth minute of injury time.
United manager Solskjaer has spoken highly of Cavanis goal for his side.
Solskjaer told United’s official website: “First of all, it\s great movement by Anthony, a great pass and a great touch to go past him on his first touch and you’ve just got to focus on hitting the corner. Keep it low, with a little bit of curve and its a top-quality strike.”
United will take on city rivals Manchester City in the semi-finals of the Carabao Cup this season.