The Spaniards had a 3-0 advantage from the first leg and Angel Correa promptly stretched their lead in the tie.
Aubameyang, who joined Arsenal in January, played for former club Borussia Dortmund in the UEFA Champions League this season.
The victory restored City’s 16-point lead at the top of the Premier League
The top four teams from England, Spain, Germany and Italy will now qualify automatically for the Champions League.
The Italians lost 3-1 at home in last week’s first leg with a performance that embarrassed coach Maurizio Sarri, although he has emphasised that winning Serie A is the priority.
The Frenchman signed a new contract at Arsenal at the end of last season but the club has shown little progress this term
Arsenal and AC Milan enjoyed 3-0 away wins at Ostersunds and Ludogorets Razgrad respectively, while Michy Batshuayi scored twice to give Borussia Dortmund a 3-2 win over Atalanta in the first of two Bundesliga-Serie A clashes
The first chance of the game went to the returning Danny Welbeck, who headed wide of the far post after meeting Mohamed Elneny's cross, while Henrikh Mkhitaryan also had an effort cleared off the line by a defender
Mourinho became the first United manager in history to win a major trophy in his first season when he secured the League Cup last year, and he also led the club to victory in the Europa League, the only competition they had never won
The Gunners will travel to Sweden for the first leg of the clash on February 15, before the return fixture takes place at the Emirates Stadium one week later