Henrikh Mkhitaryan scored his first Manchester United goal to set up a 2-0 win over Zorya Luhansk in Ukraine on Thursday and take Jose Mourinho's side into the last 32 of the Europa League.
United required only a point to secure progress from Group A but Mkhitaryan's 48th-minute strike and a late Zlatan Ibrahimovic goal separated the sides and took the Premier League club through in second place behind Fenerbahce, who won 1-0 at Feyenoord thanks to a Moussa Sow effort.
The game went ahead despite concerns about the state of the icy, rock-hard pitch at the Chornomorets Stadium in Odessa, almost 1,000 kilometres away from Luhansk in the conflict-torn east of the country.
After a goalless first half, United broke the deadlock three minutes into the second half as the Armenian Mkhitaryan burst forward from midfield through the middle of the Zorya defence before finishing past goalkeeper Igor Levchenko.
They wrapped up the victory two minutes from the end as a fine one-touch passing move ended with Paul Pogba sending Ibrahimovic away, the Swede running through and finishing coolly.
"I was waiting a long time for this goal. My next goal has to be at Old Trafford because I want to score at home," Mkhitaryan, who previously played in Ukraine for Shakhtar Donetsk, told BT Sport.
"The first half was a little bit difficult because we couldn't find the last pass but in the second half we created some space for the wingers and the strikers. The important thing was to win today and go through."
Mourinho praised the playmaker, who endured a difficult start to his United career but is now starting to show his worth.
"He worked hard physically and tactically -- the talent was there, we knew that when we bought him. Now he's playing good -- in the Premier League, Europa League and EFL Cup -- and now the goal means a little more happiness for him, so I'm very pleased," Mourinho said.
United will join Tottenham Hotspur, who drop out of the Champions League, in the last 32, but there was bitter disappointment for fellow Premier League club Southampton.
Claude Puel's men knew a goalless draw or a win at home to Hapoel Beer-Sheva would see them advance from Group K but instead drew 1-1 with the Israelis and were eliminated.
The visitors went in front in the 79th minute, Yuval Shabtai pouncing on a poor pass by Oriol Romeu and setting up Maor Buzaglo to fire home.
Virgil van Dijk equalised with a deflected shot in stoppage time but they could not get a winner and Hapoel go through instead.
A brilliant late chip by Manuel Trigueros gave Villarreal a nervy 2-1 win over Steaua Bucharest that took the Spanish club into the last 32 from Group L behind the Turkish side Osmanlispor.
Fellow Spaniards Celta Vigo won 2-0 at Panathinaikos and qualify from Group G, while Fiorentina are through as winners of Group J after a 2-1 win over Qarabag in Azerbaijan secured by a 76th-minute goal from 19-year-old Federico Chiesa, son of ex-Italy striker Enrico, who was then sent off shortly after.
PAOK of Greece are also into next week's draw for the first knockout round thanks to a 2-0 win against Slovan Liberec, while Gent joined Shakhtar Donetsk in advancing from Group H.
Kalifa Coulibaly's stoppage-time strike clinched a 1-0 win over Konyaspor in Turkey and took the Belgians through at the expense of Braga, who lost 4-2 at home to Shakhtar.
AZ Alkmaar beat Zenit 3-2 in the Netherlands and join the Russians in progressing from Group D.
Dundalk had gone into their final game in the same group away to Maccabi Tel Aviv still in with a chance of going through but a 2-1 reverse in Israel ended the Irish champions' hopes.
Romanian champions Astra drew 0-0 at home to Roma and go through with the Italians from Group E, while Sassuolo and Genk will try again in Group F on Friday after fog in Italy forced their encounter to be postponed.