Kerber defeated Barty 6-4, 6-4 to give Germany the lead and Zverev followed with a 6-4, 6-3 win over Ebden to set up a rematch of last year's final against Switzerland.
The Australian pair later combined for a consolation 4-0, 4-3 (1) win in the mixed doubles against Kerber and Zverev.
"It's nice to be back in a final. It's nice to play Switzerland as well," Zverev said.
Defending champions Roger Federer and Belinda Bencic clinched the title a year ago with a mixed-doubles win over Kerber and Zverev.
"We lost a very close match last year, and we definitely wanted to get there and compete for the title again," Zverev said.
"And that's why me and Angie decided after last year's final that we are definitely going to come back here to Perth."
Ferrer, who will be retiring at Madrid in May, defeated Lucas Pouille 6-4, 6-7 (5), 7-6 (2) in Spain's final round-robin tie.
"It's going to be the last matches in my career and I try to enjoy every point that I play," Ferrer said. "For me it's a pleasure to play here in this center court at Hopman Cup. I never played but I am happy to have the chance to play one time here."
Ferrer made an impressive debut in the Hopman Cup where he recorded an upset victory over Australian Matt Ebden and also pushed Alexander Zverev to three sets.
Former world No. 1 Garbine Muguruza earlier defeated Alize Cornet 6-1, 6-3 after putting aside a left thigh injury.
Muguruza received treatment while leading 3-0 in the first set and returned after eight minutes with her left thigh strapped.
Muguruza also went 3-0 up in the second set before Cornet broke back but eventually lost the match in straight sets.
Cornet and Pouille then provided France a consolation win when they won against Whitney Osuigwe and Ferrer 4-2, 4-2. Osuigwe replaced Muguruza, who withdrew from the mixed doubles due to a thigh injury.
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