Rashford scored twice to give United a 2-1 victory in Jose Mourinho's return to Old Trafford, taking his tally to 12 goals from 13 games.
Solskjaer told BBC Sport: "It's the best he's had under me. He was mature, strong against good Premier League players.
"His penalty was calm and composed, and his [first] goal, we know he's got those strikes in him and he had three or four chances.
"It's like he was back on the playground or in the back garden. We want them to have fun, there's nothing dangerous out there - just 75,00 people, wanting to see the best [of them]."