McTominay put in one of several impressive displays as United started their Champions League campaign with a famous victory at the Parc des Princes.
Marcus Rashford's late goal sealed a deserved three points, which only came under threat when Anthony Martial headed into his own net to cancel out Bruno Fernandes' first-half penalty.
United were otherwise largely in control, thanks in no small part to McTominay and Fred's midfield partnership, with the pair shutting down service to Neymar and Kylian Mbappé.
Solskjaer lavished praise on his midfield duo after the final whistle, describing their performances as "outstanding", particularly as McTominay had played much of the opening 45 minutes with poor vision.
"They're in good form now, they're good players and played really well against Newcastle," Solskjaer said of the Scotland international and Fred.
"They laid the foundation for the win in that game and laid the foundation for today as well.
"Scotty played the first half with one eye as well, that was the most impressive thing, because he lost his contact lens. That was impressive."
Solskjaer added: "We know when we go here against players and a team like this with players like Neymar and Mbappe we have to defend well and David will have to make a few good saves.
"We played against a fantastic team, so we have to defend well and that's the key - that the players are keen to work really hard for each other."
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