The world number seven was clinical in a 6-4, 6-4 victory over a player ranked a place above him to help put his country into a last-four clash with Australia.
Top seeds Poland, led by Iga Swiatek, meet France in the other semi-final. Both are played in Sydney on Saturday ahead of the Sunday decider of the mixed teams tournament.
World number eight Maria Sakkari continued her sparkling early season form by blasting past Angelique Kerber 6-0, 6-3 to give Greece a 1-0 lead before Zverev hit back.
It sent the tie to a deciding mixed doubles in front of a capacity crowd at Ken Rosewall Arena with Zverev teaming with Laura Siegemund to topple Sakkari and Tsitsipas' younger brother Petros 6-3, 6-3.
Zverev has won five of his six matches this week, only narrowly losing with Kerber in the German's 2-1 defeat in group play to France.
He was in full control against Tsitsipas when he led 5-3 and was 0-40 on the Greek's serve in the first set of their singles clash.
But Tsitsipas rallied to hold serve before Zverev closed out the set.
It went with serve in the second set until Tsitsipas made a string of unforced errors in the ninth game and a forehand sprayed long gave Zverev the break, and he duly sealed the win.
"I had to come out aggressive because I knew Stef is one of the best aggressive players, if not the best aggressive player, in the game," said Zverev.
"If he is on the front foot it's extremely difficult to play against him."
Sakarri was on a mission against Kerber and stormed through the first set in 30 minutes.
She didn't let up in the second, racing 3-0 clear before Kerber finally got on the board by holding for 3-1.
It fired her up and she worked her first break point in the next game. Sakkari saved it, but she earned another and converted with a return down the line.
But that fleeting glimmer of hope was quickly extinguished with Sakkari breaking straight back and serving out the match in 73 minutes.
"I was pretty clinical in the first set and through 3-0 in the second. I was very solid from the baseline doing what I had to do," Sakkari said.
"I knew Angie was going to find a way to come back and that she wasn't going to give up."
It was her third straight win of the year, without dropping a set.
In contrast, Kerber is still seeking her first win of 2024 on her return from maternity leave.
