The Norwegian has seen his side close the gap on fourth place in the Premier League to just three points, but the Red Devils still remain in sixth position - behind Arsenal on goal difference. "He is only 21 but the maturity he is showing at times is more than 21 and his work rate".
Today's victory was United's seven on the trot under Solskjaer's stewardship.
So, does Rashford belong in the same bracket as Rooney and Ronaldo?
Rooney, now playing his football in the United States, said over the weekend that the club should go all out to attract Mauricio Pochettino from Tottenham.
Solskjaer said: "He can be absolutely top class".
A United fan page tweeted the following: "How am I supposed to tell my children that Rashford really put this in the top corner from this angle with that body shape?"
Ruthless Milos Raonic sends Alexander Zverev tumbling out of Australian Open
He was warned for racket abuse after the display, which came with the German trailing 6-1, 4-1 against Milos Raonic . He found himself on the wrong side of the toss as Raonic benefitted from a number of net cords early.
"The more you score the more you believe you are going to score and everyone says when you don't score 'he is bound to score soon'. The way he works during the week is fantastic because he practises a lot". Solskjær pointed to the toughness of the Wythenshawe-born Rashford.
"He is a proper Manc", Solskjaer said.
"He's on the training pitch all the time and at times you have to drag him off, because he just wants to be out there".
The United boss had to pick his words carefully but he was clearly impressed by the way Rashford stood up for himself after needing treatment for a foul by Martin Montoya, scything the Spaniard down to earn the only booking of the game moments before he was substituted in added time.
There have been noticeable changes in form for the likes of Marcus Rashford, Victor Lindelöf and Paul Pogba, with the latter notching an impressive five goals and four assists in the six league games under Solskjaer.
"We can be even more clinical", the captain said.
Brighton improved in the second-half and got one back on 72 minutes, with Pascal Gross firing in off the bar. We didn't do that. I think [Pochettino] gets the best out of his players whether they are younger or older.