Juan Mata gave the English side the lead on 27 minutes before Ezequiel Lavezzi equalized for the home side twelve minutes later.
And on the stroke of half-time, Cavani popped up to give Napoli the lead heading into the break.
The Italian side added a third in the second-half, thanks to another by Lavezzi, securing a big win in the first-leg of their Round of 16 clash.
Napoli have a handy buffer to take with them when they travel to London in three weeks time for the second-leg.
Here is the goal: