But Thanasi Kokkinakis edged Alexander Zverev 5-7, 7-6 (4), 6-4 in a close tussle to level for Australia, meaning Germany needed to win the doubles to advance.
A Germany loss to Australia in the last of the group matches would have meant three teams ended with 2-1 records, and that would have sent Belgium into Saturday's championship decider at Germany's expense.
Kokkinakis retained momentum in the first set of the doubles, but Kerber remained composed despite a succession of unforced errors from Zverev — and taking the full brunt of a Kokkinakis forehand on her hip — to steer Germany to a 1-4, 4-1, 4-3 (3) in the Fast 4 format.
Zverev praised two-time major winner Kerber's performance, admitting he almost lost the match for Germany.
"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."
