The Red Devils moved above Spurs into sixth in the Premier League standings with a 2-1 victory on Wednesday night , thanks to a Rashford brace.
The 22-year-old took his tally for the 2019-20 campaign to nine from 15 outings, opening the scoring with a powerful drive after just six minutes before dispatching a penalty just after half-time.
Rashford's spot-kick rendered Dele Alli's 39th-minute equaliser as nothing more than a consolation for Spurs, who suffered their first defeat under Jose Mourinho.
The Portuguese made his return to Old Trafford almost one year on from being sacked by the club, and saw his new squad outplayed by an energetic and determined United outfit.
Solskjaer has faced plenty of criticism for the team's poor start to the season, but Rashford's match-winning display granted him a much-needed reprieve ahead of the Manchester derby on Sunday.
The United boss hailed the England striker's "fantastic" contribution post-match and was delighted to see him show his maturity and composure against a strong opponent.
"It's the best [performance] he’s had under me. He was mature, strong against good Premier League players," Solskjaer began. "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]."
Solskjaer added on a vital win marking the start of a "rebuilding" period for his squad: "You are always happy when you win. The boys are learning and improving all the time but tonight we were fantastic for long, long spells."
"The three points are massive for us. We’ve had too many draws this season and given too many points away from winning positions. It’s a great lesson in the last two games [Sheffield United and Aston Villa] and we came back in a great manner.
"We've started the rebuilding. We’ve made decisions that we had to and we’re looking to build this club to be better again and I can’t think short-term when I’m trying to do that.
"When we turn the corner and win three or four games on the run, they will get that Man Utd feeling again."
After facing off against their local rivals, United's focus will then shift to a final Europa League group stage fixture against AZ Alkmaar at Old Trafford on December 12.