The result leaves United level with PSG and RB Leipzig on nine points in Group H and knowing they need a draw away to the German side next Tuesday to progress to the last 16.
Victor Osimhen salvaged a draw for Napoli in his first club appearance since December as they held Barcelona in the first leg of their Champions League last-16 tie.
Lionel Messi had blasted Barca ahead with a penalty in the first half but Mbappé pulled the French champions level with a classy piece of control and finishing to complete a flowing team move also involving Marco Verratti and Layvin Kurzawa.
Raheem Sterling swept in from Kevin de Bruyne's cutback after 16 minutes as Pep Guardiola's side stamped their authority following the hosts' energetic start.