The visitors went into the break 1-0 up, but the Swedish striker scored twice in the space of three minutes in the second half to earn the points for the league leaders.
Nancy could have surged ahead on 27 minutes had Yassine Jebbour's effort not come off the crossbar.
Nine minutes later Benjamin Moukandjo shocked Parc des Princes when he headed home from close range after latching onto a rebound from his own shot.
However, Ibrahimovic restored parity for the Parisian outfit a minute before the hour mark when he turned home Jeremy Menez's pass from close range.
Then on 62 minutes the former Barcelona and AC Milan striker netted his second goal of the evening, latching onto Marco Verratti's pass to slot home.