It is Pogba's second game back with the Red Devils following a lengthy lay-off with a hamstring injury sustained in the first match against Basel earlier this season.
And Martial retains his spot after scoring in Saturday's 4-1 Premier League win over Newcastle, with only Pogba, Romelu Lukaku and Chris Smalling backing up with consecutive starts.
Elsewhere there is a recall for Marcos Rojo for a first senior start since damaging ACL ligaments in the Europa League quarter-final second-leg clash with Anderlecht on April 20, while Sergio Romero is given the gloves as David De Gea is rested. Jesse Lingard makes his 100th United appearance in place of Marcus Rashford.
Zlatan Ibrahimovic is on the bench as promised, with Mourinho revealing on Tuesday that he will look to give the Swede some 20 to 25 minutes of action as he continues his comeback from a serious knee injury.
A win or a draw will be enough for United to not just qualify but also secure top spot in Group A.
Basel XI: Vaclik; Akanji, Suchy, Balanta; Lang, Serey Die, Zuffi, Petretta; Steffen, Oberlin, Elyounoussi.
Subs: Salvi, Fransson, Ajeti, Riveros, Bua, Itten, Manzambi.
Manchester United XI: Romero; Darmian, Smalling, Rojo, Blind; Herrera, Fellaini, Pogba; Lingard, Martial, Lukaku.
Subs: J. Pereira, Rashford, Ibrahimovic, Shaw, Lindelof, Matic, McTominay.