Defeat for Jose Mourinho's side meanwhile ensures they too are left needing to pick up a point at home to the Russians next month to qualify as group winners.
United were dominating possession without applying the finishing touch and Fellaini maintained that frustrating trend when the Belgian hit the post with a close-range header from Anthony Martial's cross.
Die tried to steal the spotlight from the Swede with a 25-yard strike that drew a good stop from Sergio Romero.
Shaun Botterill GettyImages
Mourinho said: "I have to believe in this moment, and I am more comfortable, in the [Basel] manager's experience and in his vision, so in this moment I am much more comfortable than I was before".
Pogba returned with a bang on Saturday to produce a man of the match display in the thrashing of Newcastle after two months out with a hamstring problem. He was never really tested by Dimitri Oberlin, who often cut a lonely figure in Basel's red and blue.
That objective will be accomplished if United can score a point in Basel.More news: Rescuers battle waves, wind in hunt for missing Argentine sub
Mourinho is without defenders Phil Jones and Eric Bailly, while Michael Carrick remains out of action with a thigh issue.
Despite that Southgate decided against picking him for an ultimately weak squad for the draws against Germany and the Brazilian's, there are a only few months to impress ahead of World Cup in Russian Federation this Summer but Smalling stated that he will be looking to give Southgate "no choice" but to pick him. Southgate, though, appears to want more.More news: Iranian Man Charged In HBO Hack That Released 'Game Of Thrones' Script
Criticism of Jose Mourinho being defensive bemuses Ander Herrera, with Manchester United's record under the Portuguese beyond question. He is a Mourinho player, a ball victor in both boxes.
Fellaini is out of contract at the end of the season and can start talking to overseas clubs in January.More news: Uber strikes deal with Volvo
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