"We were expecting a really tough night here and we made a lot of changes again but I'm delighted to find a way to win."
Arsenal are two points clear of PSV Eindhoven, who thrashed FC Zurich 5-0. Bodo/Glimt have four points from four matches.
Scott McTominay spared United's blushes with a 93rd-minute goal in a 1-0 win over Cypriots Omonia at Old Trafford.
Omonia goalkeeper Francis Uzoho pulled off a string of fine saves to frustrate a wasteful United before the Scotland midfielder fired home in stoppage time.
"You have to be patient sometimes. Their goalkeeper was a different class but we created enough chances and deserved to score in the end," McTominay told BT Sport.
"It's a massive goal because we need to win the group."
Erik ten Hag's team stayed three points behind Group E leaders Real Sociedad, who beat 10-man Sheriff Tiraspol 3-0 to record a fourth successive win.
La Real are guaranteed to advance. They host United on November 3 in a clash likely to determine which team goes directly into the last 16.
Each of the eight group runners-up will face a team that drops down from the Champions League, in a knockout round play-off in February.
Freiburg eased to a fourth consecutive victory in Group G, piling further misery on Nantes with a 4-0 win away to the French Cup holders.
Fenerbahce and Rennes both ensured they will progress from Group B. Fenerbahce won 2-1 at AEK Larnaca, while Rennes defeated Dynamo Kyiv 1-0 in Krakow.
Belgium's Union Saint-Gilloise must wait to make sure of a place in the last 16 despite coming from two goals down in a thrilling 3-3 draw against Braga.
Union Berlin revived their hopes in Group D as Robin Knoche's 89th-minute penalty gave the surprise Bundesliga leaders a 1-0 victory over Malmo.
All four teams in Group F are level on five points. Lazio drew 2-2 at home to Sturm Graz while Feyenoord were held by the same scoreline by Midtjylland.
Ferencvaros are three points clear in Group H after beating Red Star Belgrade 2-1. Trabzonspor hammered Monaco 4-0 to climb above the Ligue 1 side into second.
Villarreal qualified for the last 16 of the Europa Conference League as winners of Group C. Senegalese midfielder Nicolas Jackson scored the only goal in their 1-0 win at Austria Vienna.
West Ham advanced from Group B following a 2-1 win over Anderlecht courtesy of goals from Said Benrahma and Jarrod Bowen.
The Hammers need just a point from their final two games to wrap up top spot.
Istanbul Basaksehir and Djurgarden will also continue their European adventure in the new year.