It wasn't a flawless day for United - they had defender Eric Bailly sent off for a reckless challenge later in the second half.
"I'm really pleased that he'll get goals". The style of play has been significantly different to that displayed during most of Mourinho's time at the club, and Pogba feels Solskjaer's tactics now have United playing how they want to.
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.
One change could be made in the back-line.
But United had to see out the final 11 minutes a man light after Eric Bailly needlessly lunged in on Ryan Fraser to see a straight red card. His talent was never in doubt, but once again he appears to be making every attempt to control the midfield, something he rarely seemed capable of before the change in manager. That's how we want to play, we want to attack and that's what we try to do on the pitch. "It's touch, pass, move", said Solskjaer. United were at their most threatening down his side, and he was beaten far too easily by Rashford for the first goal.
Against Bournemouth, United is expected to take home another three points against a club it has done very well against in recent years.
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Con Ed is still monitoring the situation saying, "All power lines serving the area are in service and the system is stable". The cause was a transformer explosion at a Con Edison power station in Astoria , Queens , about 9:30pm local time.
Pogba scored twice in Sunday's 4-1 win over Bournemouth, after a double against Huddersfield Town on Boxing Day, and he exuded confidence and positivity throughout the match and just enough diplomacy after it to avoid a direct criticism of Mourinho, with whom he had a fraught relationship.
Next up for United is a trip to Newcastle United on January 2, while Bournemouth will attempt to return to winning ways when they welcome Watford on the same night.
It was Rashford's sixth assist in 17 Premier League appearances this season, as many as he managed in his previous two seasons combined.
United have now scored 12 times in three games under the Norwegian, but Solskjaer insisted he has just tried to instill what he learned under Alex Ferguson during 11 seasons as a player at Old Trafford.
City, who had lost three of four in the league, made a fast start at Saint Mary's Stadium through David Silva, only for Pierre-Emile Hojbjerg to equalise in the 37th minute.