Parolo’s rare headed hat-trick was the first in Italy since Joaquin Larrivey achieved the feat for Cagliari in a 6-3 loss against Napoli in March 2012.
All eyes in Italy are firmly fixed on Turin however where champions and current leaders Juventus host resurgent Inter Milan later Sunday.
Second placed Napoli, three behind Juventus on 48 points, trounced Bologna 7-1 on Saturday in a game where Marek Hamsik and Dries Mertens ran riot with hat-tricks.
Struggling AC Milan suffered a fresh blow with a 1-0 home defeat to Sampdoria on Sunday, their third straight league defeat, that made a return to the Champions League more distant.
The once mighty Milan sit 10 points behind Roma in the third and last Champions League qualifying spot and are now 14 points behind Juventus, who have two games in hand.
Roma can also stretch their lead with a win over Fiorentina on Tuesday.
It was Sampdoria’s first win over Milan since 2012 but the Genoa side have now claimed two major scalps in succession having edged Roma 3-2 last week when Luis Muriel — who scored Sunday — also hit the winner.