The Colombian striker started ahead of the suspended Antonio Di Natale and got the visitors off to a flier after 12 minutes.
© AP Photos
Muriel opened his account with a precise curling strike into the far corner after strong approach play from Polish teenager Piotr Zielinski.
Parma struggled to find a response and went further behind on 62 minutes courtesy of a simple finish from Roberto Pereyra.
The visitors controlled the closing stages to keep a clean sheet and move to eighth in Serie A with a 3-0 victory.