The Italy forward notched her first after two minutes but had to wait to the cusp of half-time, by which time Lineth Beerensteyn had already put Juve 2-0 up, before striking in her second from the spot.
The 32-year-old completed her hat-trick in the 57th minute after some fine link-up play from Beerensteyn and Barbara Bonansea before adding her fourth from the penalty spot two minutes later.
Zurich had Irina Pando sent off six minutes from time for a late tackle on Beerensteyn that earned her a second yellow card.
The win took Juventus second in Group c on eight points, two behind Arsenal and one ahead of Lyon, who play later on Thursday.
Get all of the statistics from the match here!
Bayern Munich are on the brink of qualifying after a comprehensive 4-0 win at Swedish side Rosengard.
Bayern struggled to break down the home defence until a looping header from Brazilian defender Tainara gave them the lead in the 38th minute.
Sydney Lohmann doubled the lead in the 66th minute with Georgia Stanway and Julia Landenberger following up to complete a comfortable win.
Bayern go top of Group D although Barcelona can reclaim top spot if they beat Benfica later on Thursday. A Benfica victory would leave the Germans needing at least a draw when they host the Portuguese next week.
