The Norwegian emulates the feat of Sir Matt Busby in 1946.
Rashford doubled the lead after a sweeping move involving Lukaku and Alexis Sanchez as Newcastle lost for the eighth time at home in the league this season.
Newcastle’s best chance fell to Ayoze Perez when the Spanish forward got behind the visitors’ defence but Luke Shaw made a last-ditch challenge.
The hosts were fortunate to finish the game with 11 players after substitute Jonjo Shelvey’s reckless challenge from behind on Paul Pogba, which went unpunished.
After convincing wins over Cardiff, Huddersfield and Bournemouth, this was Manchester United’s sternest test under Solskjaer.
They lost the corresponding fixture last season 1-0 but came through this examination while keeping a first clean sheet in eight top-flight matches.
This was another high-octane, attacking performance from a team that has come alive under the caretaker manager.