Zlatan Ibrahimovic's free-kick was deflected past Thibaut Courtois, thanks to John Mikel Obi's outstretched leg. But the Nigerian midfielder made amends shortly before the break, with a fine finish inside the box to level matters.
However, Edinson Cavani came off the bench to grab the winner, tucking home Angel Di Maria's lovely pass.
In the other game of the night, Jonas scored the only goal as Benfica beat 10-man Zenit 1-0 at home.
