Sebastian Giovinco eased the hosts' nerves after 24 minutes with an expertly taken free-kick to notch his 12th goal of the campaign.
Radja Nainggolan fouled Jonathan in the penalty area after 71 minutes, giving Sergio Floccari the chance to double Parma's lead. The 30-year-old confidently swept the ball home to put Parma firmly in the driving seat.
Okaka Chuka dusted himself off and took the resulting penalty, making it 3-0 and three points for the home side.
Parma rocket to tenth in the table, while Cagliari remain just four points ahead of 18th-placed Lecce.