Mourinho was back on the touchline 352 days after his sacking, but suffered his first defeat in charge of Tottenham after Marcus Rashford's brace.
Rashford scored in the sixth minute and then slotted home a second-half penalty to earn a 2-1 win and ease the pressure on Mourinho's successor, who had overseen their worst start to a season since 1988.
Mourinho would have fancied a win after Dele Alli's brilliant equaliser just before the break, but his side were second best.
"It was one of the best, we have had spells against Liverpool, Chelsea, Leicester of course, but for 40 minutes we were excellent," Solskjaer said of his side's display.
"But the reaction after they scored was also good. It is always a concern because so many times this season we have been winning, gone into a draw and stayed in a draw, but they never gave in, trusted themselves and I think we deserved to win."
It was Rashford who ensured he would be in the headlines with his match-winning display and Solskjaer was delighted to see him play with freedom.
He said: "The boy is 22 and today he played like he was in the garden or in the back yard or in the playground with his mates.
"He has just enjoyed himself. Sometimes there is expectation or pressure on him because we do expect a lot from him because he has shown it so many times.
"We want them to go out and enjoy themselves, with no fear of losing. United fans love to see wingers and forwards play with courage.
"You can define players by making things happen, movement, decision making, and he can go inside or out.
"I'm very happy with how he's matured. We want him to but it's natural he can't have this level as this was a top-class performance."