It wasn't a flawless day for United - they had defender Eric Bailly sent off for a reckless challenge later in the second half. "That's how I celebrate my goals".
"I know the club want them to sign, of course, because they are top-quality players", said Solskjaer. His two goals aside, his movement and passing repeatedly caused Bournemouth problems.
With less than five minutes on the clock, Rashford showed what he's capable of after producing a moment of magic as he bamboozled the Bournemouth defence with some stunning foot-work before setting up Paul Pogba with a pin-point cross to give the Frenchman the simple task of tapping home the opening goal.
Michael Regan Ole Gunnar Solskjaer has continued his winning start as Manchester United's caretaker manager
Victory over Bournemouth would see Solskjaer become only the third United manager to win their first three matches. "It's touch, pass, move", said Solskjaer.
The France global feels a lot has changed in the two weeks since the former striker was appointed until the end of the season, as they have adopted an attacking style which suits the players at their disposal. He rarely offered anything going forward from his wing-back role, either.
They are now just three points behind fifth-placed Arsenal and looking to claw their way back into the race for a top four finish this season.
Manchester United ended the year on a high, as they beat Bournemouth 4-1 at Old Trafford on Sunday afternoon.
It was Rashford's sixth assist in 17 Premier League appearances this season, as many as he managed in his previous two seasons combined.
They have scored 12 goals in that stretch - having averaged less than two per game under Mourinho - with Pogba netting two for the second game in a row. Solskjaer, however, unlike his predecessor, seems happy to counter this by encouraging his team to try to score more goals, not just by bringing on Marouane Fellaini.
Trump threatens to close Mexico border if funding for wall not approved
Trump fired Twitter barbs at Democrats on Saturday as talks to end a weeklong partial government shutdown remained at a stalemate. But that won't accomplish anything unless Trump and the Republican-controlled Senate go along with it.