The Red Devils moved up to third in the Premier League, within five points of leaders Liverpool with a game in hand, thanks to an emphatic 6-2 triumph on Monday (AEDT).
Scott McTominay scored the competition's earliest ever brace in the first 170 seconds, while Bruno Fernandes and Victor Lindelof also netted before half-time.
Daniel James and Fernandes, this time from the penalty spot, were on target after the break, helping Manchester United score six in a league game for the first time since thrashing Arsenal 8-2 in August 2011.
"That was fantastic," Solskjaer told Sky Sports. "From the first minute we had a plan to get after them, go forward when we got the ball, and of course Scott gets two goals in the first three minutes - a great start to the game.
"Just imagine if that had 75,000 people here - it would have gone down in history as one of the great Manchester United performances against Leeds at home."
Manchester United managed more goals in the first half against Leeds than they managed in their first six home Premier League games of the season (three), winning only one of those fixtures.
Solskjaer's side scored from six of their 26 attempts, 14 of which were on target, in an end-to-end match that saw 43 efforts in total - the most in a Premier League match this season.
"You have to earn the right to win it by running even more than them. That's the challenge against Leeds, who are one of the fittest teams in the league," Solskjaer said.
"They man-mark, of course, so there was a couple of moves that we worked on, which worked at times. It should - it could - have been 12-4.
"You know it's going to be frantic, hectic against them. No matter what the result, whether you're up 5-0 or 5-0 down, they have a certain attitude and style that makes you have to work, have to concentrate every minute."
James, who was on the brink of joining Leeds from Swansea City in January 2019, was handed a first Premier League start in two months and scored his first goal in the competition in 33 appearances.
He covered more distance and managed more sprints than any player on the pitch, which Solskjaer hopes is a sign of things to come from the Wales winger.
"The goal will give Dan James a lot of confidence," Solskjaer told BBC Sport.
"He's been biding his time, been patient, been working hard and he's still as fit as a fiddle and I was very, very pleased for him."
However, McTominay stole the headlines with his early double, profiting from some sloppy Leeds play as the visitors struggled to adapt to the fast-paced nature of the game.
"It was a good game for me," McTominay told Sky Sports. "I'm used to playing high energy, high-tempo football matches. For us as a team, I thought we played really well today and deserved the six goals.
"Everybody knows with Leeds that they are an amazing team with an amazing coach. I feel like the detail they go into both on and off the ball is high, and we knew it as well. We've done a lot of analysis on them.
"For me, I feel like the manager fully trusted me to do a job today and obviously it pays off when you get six goals."
United legend Gary Neville compared McTominay to a mixture between Roy Keane and Paul Scholes while on commentary for Sky Sports, but the Scotland international refused to get too carried away.
"You just go on the pitch to do your job. It's nice to score two goals and the team did a really good job," he said.