Man United tore visitors Leeds apart at Old Trafford in a 6-2 success, with the first two goals coming inside three minutes.
McTominay scored both, the earliest brace ever in the competition, as he turned in a dominant individual display.
The Scotland international also assisted Daniel James for the fifth goal from one of three chances created, while he covered 10.8 kilometres - third-most among Man United players - and weighed in defensively with a game-high five clearances.
Although McTominay hobbled off in stoppage time, nursing a groin issue, Solskjaer pointed to the player's immense energy at the heart of the team as key; the notoriously hard-working Leeds ran only 2.6km further than the Norwegian's side.
"We knew they have high energy and intense moments," the manager said.