Australia levelled the tie after Thanasi Kokkinakis upset world number four Zverev 5-7 7-6(4) 6-4, leaving Germany facing a must-win mixed doubles match to progress to the final.
Kokkinakis helped Australia to win the first set of the doubles but Kerber maintained her fiery dominance to steer Germany to a 1-4 4-1 4-3(3) victory.
"Angie played unbelievable in both of her matches — she's the reason we're in the final," Zverev said. "I'm going to give all the credit to her. I didn't play my best today — luckily I have an unbelievable partner."
Earlier, Belgium whitewashed Canada 3-0 and were on course to reach the final as group winners before Germany's victory led them to the top.
Elise Mertens beat Canada's Eugenie Bouchard 6-4 6-4 to hand Belgium the advantage and David Goffin sealed the tie for the European side with a 6-2 6-4 win over Vasek Pospisil.
Germany last won the Hopman Cup in 1995 and in Saturday's final they will face an all-conquering Swiss team with Roger Federer and Belinda Bencic yet to lose a match in the tournament.
(Reporting by Aditi Prakash in Bengaluru, editing by Pritha Sarkar)
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