Earlier, Spain defeated France 2-1 in their final round-robin encounter as former world number one Garbine Muguruza beat Alize Cornet 6-1 6-3 before veteran David Ferrer battled past Lucas Pouille 6-4 6-7 (5) 7-6 (2).
But Kerber levelled the tie with a 6-4 7-6 (8-6) win over Bencic in the women's singles rubber.
The Swiss have now won the Hopman Cup on four occasions, with Germany unable to halt a 24-year wait to lift the trophy.
Federer's performance-level was "the flawless 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".
"I hope it (final) is going to be just as exciting as previous year, but just going the other way".
Federer said the win helped atone for a loss to the German in the semi-finals of the season-ending ATP World Tour event in London.
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He broke Zverev in the 10th game of the first set and then tightened the noose on the German, with two more breaks in the second set.
"It was a good Match for me, no doubt about it", he said, and stressed: "I have well-pitched". Its place in the calendar is under threat from the ATP Cup, a men's only team event which is set to launch in January next year. The last point was won by Sakkari that surprised Federer with a fantastic backhand and Stefanos couldn't contain his joy repeatedly hug and kiss Maria on court.
The German's serve is big-and here he maintained a near constant speed of over 200kph-but the more nuanced and accurate serving of Federer ensured the Swiss dropped only two points on his serve in the entire first set.
However, a bad service game in the seventh game of the opening set handed the early ascendancy to Kerber, who won the first set in 32 minutes, and then snared an early break in the second set.
Teammate Matt Ebden needed to win his match to keep Australia's hopes alive but went down to Zverev 6-4 6-3.