World No.9 Fritz cantered through their Monday morning clash in just 64 minutes in Sydney.
Compatriot Madison Keys then beat Jule Niemeier 6-2 6-3 to secure the United States' passage into the next round of the new mixed teams event.
After defeating the Czech Republic 4-1 in their opening tie, the Americans only needed two points from Germany to ensure top spot in their group.
They will complete their tie against Germany on Tuesday before facing fellow group winners Great Britain for a place in the final four, also to be played in Sydney from Friday.
Zverev is playing for the first time since tearing three ligaments in his right ankle against Rafael Nadal in a French Open semi-final in June.
Now ranked No.12 in the world, his first match was a straight-sets loss to the Czech Republic's world No.81 Jiri Lehecka on Saturday.
Big-hitting Fritz was a step up again and quickly exposed the German's lack of mobility and match fitness, losing only one of 27 points when landing his first serve.
"I felt pretty good; it was tough to judge my level because I do feel like he's coming back from injury, he's a bit rusty," Fritz said.
"He was giving me a good amount of free points ... I'm sure it won't take him too long for him to fully get his form back.
"It's great to start the year off with some wins, for sure. The confidence aspect of tennis is super important, Especially going to Australian Open off an off-season."
In Perth, three-time Australian Open semi-finalist Stefanos Tsitsipas squared Greece's tie with Belgium 1-1, impressive in beating David Goffin 6-3 6-2 to move them within one victory of securing a city final berth.
Alison Van Uytvanck defeated Despina Papamichail earlier in the day, 7-5 2-6 6-3 to put Belgium ahead.
France and Croatia began their tie in the evening session to decide top spot in their pool.
Italians Martina Trevisan and Lorenzo Musetti both won their singles matches against Norway to secure their passage to the city final in Brisbane.
Meanwhile, women's world No.1 Iga Swiatek downed Switzerland's world No.12 Belinda Bencic 6-3 7-6 (7-3) in Brisbane.
Marc-Andrea Huesler levelled the tie for the Swiss with a 6-3 6-2 win over Daniel Michalski.
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