The eight-time champion moved seamlessly into the quarter-finals with a 6-1 6-2 6-2 victory which took just an hour and 13 minutes.
Federer will bring up his century of triumphs if, as looks increasingly likely, he reaches the semi-finals.
Not many of the previous 98 could have been this straightforward, so powerless was Berrettini to even threaten the Swiss.
Federer was a break up inside 10 minutes, and had the first set wrapped up within 17 in a painful opening for Berrettini.
Things did not improve much for the Italian in the second, the dreaded Mexican wave breaking out as the crowd made their own entertainment once Federer had the set in the bag after three quarters of an hour.
Berrettini's humiliation was complete when, facing yet another break point in the third, he misjudged the spin on a Federer return, swatted at thin air and fell in a heap on the grass.
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