The Giallorossi were made to wait until the second half to break the deadlock, as midfielder Bryan Cristante continued his fine recent run of form with a pinpoint header from a corner just before the hour-mark.
And that moment would prove decisive, as substitute Lorenzo Pellegrini would play in Cengiz Under soon afterwards for the clinching goal.
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The result means Eusebio Di Francesco's side ended 2018 with back-to-back league victories, pushing them up to fifth in the table at full-time.
They now have two weeks before their next encounter, against Virtus Entella in the Coppa Italia.
Parma fought valiantly for long spells at the Stadio Ennio Tardini, with goalkeeper Robin Olsen making one outstanding save from Luca Siligardi with the scores still 0-0.
But the Giallorossi were on top throughout - with Edin Dzeko testing Luigi Sepe time and time again - and deservedly took the lead through Cristante.
That intervention seemed to calm the side and allow them to play a more expansive, incisive style of football - and the second goal soon after was the least they deserved for their efforts.
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