City's win may not have been as emphatic as Liverpool's magnificent 5-0 victory here in United's last home league game but the gulf between the sides was certainly as wide.
Solskjaer and United got off to the worst possible start when Eric Bailly turned Joao Cancelo's cross into his own net after seven minutes and it was only the brilliance of keeper David de Gea that somehow kept City at bay until the final seconds of the first half.
De Gea produced a string of brilliant saves, denying Cancelo twice as well as Gabriel Jesus and Kevin de Bruyne, plus even saving from his own defender Victor Lindelof. However, Bernardo Silva took advantage of awful defending from Harry Maguire and Luke Shaw to steal in on another Cancelo cross at the far post.
United's only response was a volley from the subdued Cristiano Ronaldo. The second half was merely a formality as City moved down the gears but still looked more likely to score in what was another chastening afternoon for Manchester United and their manager.
City boss Pep Guardiola told BBC Sport he wanted to give a "massive compliment to the players" because "they are the real artists for the way we played".
Guardiola said City's approach was shaped by United's ability on the counter-attack, adding: "If you don't finish the attack you will be attacked much, much quicker and that is where they are so good. That is why we needed a game with a thousand million passes. We need a game like with the ball in the fridge, keep it there.
"Right now Chelsea are unstoppable. We know we cannot drop much points to be close to them but against the big six we performed well."
The result took City above Liverpool into second in the Premier League while fifth-placed United are nine points behind leaders Chelsea.