Federer consolidated that advantage with another break in Zverev's opening service game of the second set, able to close out the first match of the tournament decider.
The Swiss closed out the encounter with his second match point to take the second set 6-2 and give Switzerland a 1-0 lead in the tournament showpiece.
It was Switzerland's fourth title overall, behind only the United States with six, and Federer first won the Hopman Cup back in 2001 when he teamed with Martina Hingis.
Switzerland are the champions of the 2019 Hopman Cup.
Federer's performance-level was "the ideal preparation for the Australian Open", according to CNN, and the 20-time Grand Slam champion himself described "the whole match and the whole week" as one giant "thrill". "Playing here as a team with your partner, playing the mixed which is exciting, I will miss it". The tournament is a unique event on the tennis circuit, one that features the rare showcase of mixed doubles matches with major tennis stars.