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The hosts, who came into tonight's game with just one win to their name this season, made a dream start by edging ahead with less than five minutes played.
Joel Obi jumped highest to force Antoni Mirante into action shortly after to deny the Nerazzurri, while Zdravko Kuzmanovic squandered a brilliant opening shortly after as he sent his header wide of the target.
Inter continued to push for a leveller as half time approached, but they were unable to create any clear-cut openings as Parma went into the interval ahead.
Kuzmanovic saw his long-range drive fly over the bar on the hour mark for the desperate visitors while Mateo Kovacic could not quite find the target at the end of his run.
Despite Mazzarri's charges piling on the pressure, De Ceglie doubled Parma's lead with his second goal of the night 15 minutes from time by tucking home a rebound.
Abdelkader Ghezzal could have put the icing on the cake for the Crusaders, but his miss from inside the area did not matter in the end, with Parma holding onto their shock 2-0 victory, which lifts them up to 18th place.