Matheus Cunha, Bruno Fernandes, Benjamin Sesko and Lisandro Martinez all scored in the 4-0 rout of Azerbaijan's Sabah.
It was the Red Devils' first game in the Champions League since December 2023.
Cunha fired United ahead at Old Trafford in the 27th. Fernandes and Sesko made it 3-0 by halftime and Martinez scrambled home a fourth after the break.
In Munich, Jamal Musiala scored in his first start of the season, Michael Olise had a brace and Harry Kane was also on target as Bayern Munich routed Bodø/Glimt 5-0 to extend their extraordinary start and home record in the Champions League.
Germany player Musiala had missed previous games after collapsing due to absence seizures in two pre-season friendlies, with his medication now adjusted.
Musiala opened the scoring into the far corner in the 47th minute and Kane headed home in the 61st for his 55th Champions League goal.
Superb strikes from Alphonso Davies in the 77th and Olise in the 83rd and a final stoppage time effort from Olise completed a big win. Bodø had Odin Bjørtuft sent off late.
Six-time champions Bayern recorded their 23rd straight win in a Champions League opener since last losing a first match in 2003 against Deportivo A Coruna.
Bayern are unbeaten in 39 Champions League home games, of which they have won 37, since a December 2013 defeat against Manchester City.
Italy's Como claimed an impressive 4-1 over RB Leipzig in their first ever Champions League match, with Martin Baturina, Tasos Douvikas, Assane Diao and Maximo Perrone on target.
Slavia Prague seemed on course to victory over Lens despite having Mikulas Konecny sent off two minutes after coming on for the second half when Danijel Sturm completed a brace for 2-1 in the 87th.
But stoppage time goals from Florian Thauvin and Ruben Aguilar gave Lens an improbable 3-2 win.
PSV Eindhoven drew 1-1 with Shakhtar Donetsk, as did Fenerbahce and Roma in Istanbul, where there was drama.
Fenerbahce head coach Ismail Kartal announced his resignation after the match, but minutes later the club president said Kartal would stay in the job.
The 65-year-old Kartal told a press conference he was leaving "never to return", adding he had taken the decision "to clear the way for the club".
Minutes after the press conference, Fenerbahce president Aziz Yildirim told reporters Kartal "continues in his role".
"Some fans threw a bottle at the coach's head this evening during the game. He is upset about it," Yildirim said.
"I just spoke to Ismail Kartal. He mentioned the bottle incident and he also complained about being under pressure."
Asked if Kartal had told him that he would stay, Yildirim said: "There's no need for him to say (openly) that he'd continue. I am his senior, I told him to continue and that's it. We are a family."
with agencies
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