The Frenchman's 60th-minute thunderbolt, before he layed on a second for the Argentine in the 86th minute, ensured the English champions did not suffer another frustrating early exit in Group E.
City's great escape into the last 16 seemed unthinkable when they trailed in their penultimate game at home to Bayern Munich with just five minutes remaining before Sergio Aguero completed his famous hat-trick.
Victory or a score draw offered City's most realistic chance of progressing from the group behind Bayern Munich in a fevered atmosphere in Rome and even without their injured totem Aguero, Manuel Pellegrini's men produced a performance full of resolve.
Nasri, given too much space on the edge of the box, hammered a glorious 20-metre shot which cannoned off the post and into the net, and City defended manfully before Nasri freed the rampaging fullback Zabaleta to score his first Champions League goal.
