Under the short sets format, the match is decided by a winner-takes-all point if scores are locked at 4-4 in the third-set tiebreak.
Germany blew a championship point before it reached that stage, and they again faltered when everything was on the line, with Zverev hitting the ball into the net to spark Switzerland's celebrations.
Federer's three Hopman Cup titles is more than any other player. The 20-time grand slam champion first won the Hopman Cup in 2001, when he teamed with Martina Hingis to beat the US.
The 37-year-old won his second crown alongside Bencic last year, beating Zverev and Kerber.
And it was the exact same script this year, with Federer winning his singles match in the final before helping clinch the deciding rubber in the mixed doubles.
The crowd was appreciative of Switzerland's achievement but Zverev roasted Federer when given his chance with the microphone at the trophy presentation after the tie.
"We're all tired of you guys already, but what can we do?" Zverev said as those inside the stadium roared with laughter. "Especially you (pointing at Federer). I mean, you're 30-whatever. Why? Just why?
"Let us have one — just the Hopman Cup, man. Just once."
That spray made Federer and Bencic lose it, prompting Zverev to continue playing bad cop.
"What the hell are you laughing at right now?" he said as the laughs kept flowing.
Federer tried to shift the blame. "She did it," he said, pointing at Bencic and making it clear she was making him laugh.
Zverev added: "What a nice guy, huh?"
Federer tried his best to look as serious as possible and keep a straight face so as not to "offend" his German rival again, but it wasn't long before his smile broke back out.
Saturday's final took on extra significance given there's a strong chance it will be the last ever Hopman Cup.
A new ATP World Team Cup tournament is set to be introduced in Australia next year, with the Hopman Cup almost certain to make way for the 24-team event. Federer beat Frances Tiafoe, Stefanos Tsitsipas, Cameron Norrie, and Zverev in straight sets at the Hopman Cup, giving him an excellent preparation for his Australian Open title defence.
"I'm happy I'm feeling this good and playing as well as I am," Federer said. "It's good to finish on a singles performance like this. I'm a bit surprised that the matches have gone as well as they have."