Rudi Garcia's men have endured a tough 2015 and had won just three league matches this year leading up to Saturday's contest, a run that has halted their title bid and left them battling to play in Europe's premier competition next season.
But Pjanic rounded off a fine team move in the 25th minute as Roma earned back-to-back victories, while goalkeeper Morgan De Sanctis also impressed as a frustrated Napoli failed to win for a fifth straight league game and saw their own Champions League prospects dented.
Pjanic delivered a warning in the 20th minute when his free-kick from the left evaded everyone and brushed the outside of the far post, but the midfielder was celebrating five minutes later when he coolly slotted home Alessandro Florenzi's cutback.
Napoli saw claims for a penalty turned down when Kostas Manolas slid in to block a Jonathan de Guzman shot, with the visitors suggesting the defender had used his hand.
Rafael Benitez's team saw several chances go begging after the break, as Dries Mertens failed to get enough power on a poked effort that De Sanctis saved low to his left, before the Roma keeper made a fine stop to tip Manolo Gabbiadini's volley over the crossbar.
Juan Iturbe had the chance to complete the win for Roma as the clock wound down when he shot wide after rounding Mariano Andujar, but it made no difference as Roma claimed a vital three points.
