Pogba only managed one double in the Premier League in two-and-a-half seasons under the Forgotten One Jose Mourinho, yet he has achieved that feat twice under Solskjaer.
He opened the scoring with a close-range effort after a superb, mazy run by Marcus Rashford before heading home the second to take his haul under the Norwegian to four goals and two assists.
Rashford scored the third his efforts deserved before Nathan Ake headed home on the stroke of half-time to deny United a rare clean sheet.
Romeu Lukaku scored the fourth within two minutes of coming on when he assistant referee failed to spot he was offside.
Eric Bailly was the only blot on United's copybook when he was sent off for a late challenge on Ryan Fraser.
Here are five talking points from Old Trafford...
1. The real Pogba stands up again
Paul Pogba can be the new Captain Marvel. Bryan Robson was here in his role as a United ambassador and he would have recognised much of Pogba’s excellent play.
Robson was the archetypal box-to-box midfielder and Pogba, liberated since Jose Mourinho’s sacking, is playing that way. Not only did he pop up in the Bournemouth box to score his two goals, he got back make a fine challenge on Jordon Ibe in his own penalty area to win possession.
Pogba is finally looking like the huge talent he undoubtedly is and he has scored four goals and made two assists in Ole Gunnar Solskjaer’s three matches in charge.
2. Bournemouth's dodgy defending
Bournemouth need to be more resolute. This loss was Bournemouth’s eighth in 10 Premier League games and their sixth in succession on the road.
As laudable as Eddie Howe’s open style is, they are just too easy to play against and United simply gobbled them up.
OK, they are not in danger of being sucked into the relegation fight, but they are not going to finish in the top half of the table as they deserve if they carry on like this.
The Cherries have now been battered by Liverpool, Tottenham and United and they must have a bit more steel. United sliced through them with ease at the back and they need to be stronger defensively.
3. No more Fellaini?
Marouane Fellaini has been demoted by Ole Gunnar Solskjaer.
Fellaini perhaps unfairly came to symbolise what United fans did not like about the team’s style under Jose Mourinho.
Too often Mourinho would turn to the tall Belgian in a sign that he intended to be physical and direct.
Solskjaer doesn’t do physical or direct and instead has left Fellaini on the bench for his first three games in charge as he instead goes with more technical, ball-playing midfielders.
He only used him for three minutes of his first two games and the Norwegian clearly wants to go in a different direction to Mourinho.
4. Top four out of sight?
A top-four finish still looks tough for United. Mourinho contributed to his sacking by predicting last month that United would end the year in the top four.
He never got close and despite Solskjaer winning his first three games in charge, United finished 2018 eight points outside the Champions League places.
Although United are playing better and have closed in on Arsenal, the likes of Chelsea and Tottenham are still picking enough points to maintain a healthy advantage over them.
United still have the second half of the campaign to catch them, but it is going to take some doing.
5. Not all roses for Ole
United have work to do defensively. As breathtaking as United were at times going forward, they still look dodgy at the back.
Ole Gunnar Solskjaer did not look happy walking off at half-time after Nathan Ake pulled one back for Bournemouth because United had blown their chance of a rare clean sheet.
They have managed just two in their 20 Premier League games and for all their dominance, Bournemouth had too many threatening moments.
Solskjaer knows he has work to do yet and making United better defensively will be next on his to-do list now that he has got them playing fluently.
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