Unbeaten in his three singles matches in the tournament prior to the final as he prepared for his Australian Open title defence, the 19-time Grand Slam champion dropped the first set against Zverev, but recovered to win in three sets, 6-7 (4/7), 6-0, 6-2.
It gave Switzerland a 1-0 lead in the final, with Federer aiming to add to the title he won in Perth with Martina Hingis in 2001.
However, the young German managed to prevail in the tie- breaker as he aimed to repeat his singles win over Federer at the Hopman Cup last year, when all three sets were decided by tie-breakers.
Federer's frustration was obvious, dropping his racquet after missing an easy volley and then launching a ball towards the roof.
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However, it soon passed as he started to blunt the German's power and his superior court craft turned the momentum.
Federer took pace off his shots and used the drop shot repeatedly to catch Zverev out, racing through the second set.
Zverev's serve, and resolve, was broken in the third game of the third set and fittingly it was a Federer drop shot which sealed the win.
"I played great throughout the three sets and Sasha probably dropped his level a little bit in the second and third sets," he said.
"I was able to put Switzerland ahead so I am very happy.
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