United hit the post through a deflected shot from substitute Donny van de Beek late in the game but Solskjaer’s 100th game as manager ended in a defeat which leaves them in 15th place with just seven points from six games.
Arsenal move up to eighth on 12 points.
Solskjaer opted to start with Pogba in a Premier League game for the first time since their 6-1 defeat by Tottenham Hotspur last month but neither he nor the most advanced midfielder Bruno Fernandes were able to get a firm grip on the game.
Mason Greenwood forced a save out of Arsenal keeper Bernd Leno, from a tight angle in the 21st minute, but the Gunners pinned United back for long stages with their impressive pressing.
Arsenal’s Brazilian winger Willian clipped the crossbar in the 39th minute and Aubameyang drifted a shot just wide after the interval.
But Pogba’s ill-advised challenge decided the outcome and left Solskjaer with some more thinking to do about how best to organise his midfield.
“It’s hard to put your finger on it. It was disappointing from us. It was a cagey game, a game of few chances,” said United skipper Harry Maguire.
“We needed to do more, we needed to create more. It’s not good enough, we’ve got to go work hard tomorrow at training. We can’t find excuses, we’ve got to look within.”
It was also a good day for the Gunners’ North London rivals, with Gareth Bale coming off the bench to head the winner for Tottenham Hotspur in a 2-1 victory over Brighton & Hove Albion, his first goal since returning to the club from Real Madrid.
The Welshman was brought on in the 70th minute and three minutes later he met a Sergio Reguilon cross with a firm and well-directed header to restore Tottenham’s lead.
Harry Kane had put Spurs ahead in the 13th minute from the penalty spot after Adam Lallana was ruled to have fouled him as he climbed for a header.
Brighton responded with a long spell of good possession football as Spurs failed to drive home their advantage and Graham Potter’s side drew level in the 56th minute.
Southampton have done an impressive job of bouncing back from their opening two Premier League defeats to break into the top four after Sunday’s 4-3 win at Aston Villa, manager Ralph Hassenhuttl said.
Having suffered a 1-0 defeat at Crystal Palace and a 5-2 home drubbing by Tottenham Hotspur, the Saints quickly turned around their fortunes by winning four of their next five games.
That run included a 3-3 draw at an expensively assembled Chelsea where Jannik Vestergaard, one of the scorers at Villa Park, netted a stoppage time equaliser.
“The first two games at the start of the season were a disaster,” Austrian Hassenhuttl told the BBC.
“But we showed a good reaction and now we play how we should. It’s good to see how the guys are developing. It’s a good message from the boys.”
James Ward-Prowse curled in a pair of free kicks on his 26th birthday after setting up Vestergaard’s opener, and Danny Ings made it 4-0 near the hour mark before Villa took advantage as Southampton eased off.
Meanwhile, Everton boss Ancelotti may have created a goalkeeping headache for himself in Sunday’s 2-1 defeat by Newcastle as Swedish back-up Robin Olsen put in an excellent debut performance between the posts in place of Jordan Pickford.
Having arrived on loan from Roma on October 5, the vastly experienced Olsen got his first chance to show what he could do and pulled off some superb reflex stops to save face as Everton slumped to their second straight defeat.
With Ancelotti saying before kickoff that he would reinstate Pickford for next week’s visit of Manchester United, he may well have inadvertently put pressure on the England international, who has made some costly errors so far this season.
“I wanted to give an opportunity to Robin, to be part of this group and team. After this, Jordan will be back. Robin will play again but not against United,” Ancelotti told the BBC following the final whistle.
“Robin did well, he did his job. He deserves to play. Jordan will be back, we have two really good keepers and this is what we need. Robin will play again. I don’t know when but next game, Jordan will be back.”
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