World No.2 Zverev pulled out of Wednesday's tie at Perth's RAC Arena as a precaution citing a minor biceps niggle.
Kazakhstan shot out to a 1-0 lead after world No.6 Elena Rybakina posted a 6-3 6-1 win over Laura Siegemund in the women's singles.
Zverev's replacement, world No.254 Daniel Masur, threatened to pull off an upset in the men's singles as Alexander Shevchenko began to wilt in the 36C heat.
But Shevchenko overcame his physical struggles to post a gutsy 6-7 (7-5) 6-2 6-2 win and secure a place in the semi-finals for Kazakhstan.
Germany won the dead rubber mixed doubles contest 6-2 6-2.
Shevchenko had a medical assessment due to heat exhaustion while leading 1-0 in the second set of his singles match, and he questioned why the roof stayed open in such oppressive heat.
"After the match, I was feeling like I was going to die," Shevchenko said.
"They were brutal conditions. I don't understand why we are not closing the roof in these conditions, because it's quite dangerous if you're going long matches with this heat.
"I had a headache, shortness of breath - everything.
"The more concerning was the head was spinning - dizzy. So my concentration was off.
"But it got better because I switched up my game as well. I started to play more aggressively."
Zverev looked in ominous touch on the way to posting a straight-sets win over Brazilian Thiago Monteiro in Germany's tournament opener on Sunday.
But late in the third set against China's Zhizhen Zhang on Monday, Zverev could be seen stretching out his right arm.
Zverev fought on to post the 2-6 6-0 6-2 victory, but he was unable to back up for Wednesday's clash.
Despite not featuring in Germany's quarter-final loss, Zverev isn't in any doubt for the Australian Open.
Elena Rybakina blasts a forehand against Laura Siegemund in Perth. (AP PHOTO)
Rybakina put Kazakhstan in the box seat against Germany with a 64-minute rout of world No.80 Siegemund.
The 2022 Wimbledon champion converted four of her seven break-point opportunities across the match, and fired six aces to nil.
Siegemund committed 22 unforced errors and wasn't able to convert either of her two break-point chances in a match that began in 30C heat.
"I don't like when it's too hot. But the only good thing at 10am (WST) it's not as hot," Rybakina said.
"But definitely I'm trying to drink more water and stay in the shade whenever I have a chance."
In Sydney, world No.2 Iga Swiatek and Hubert Hurkacz launched Poland to the quarter-finals after a 7-6 (7-3) 6-3 win in the mixed doubles.
Quarterfinalists ✅— United Cup (@UnitedCupTennis) @iga_swiatek and @HubertHurkacz get the dub for Team Poland over Team Czechia and secure their spot in the quarterfinals! #UnitedCup pic.twitter.com/JLsN0jFs5oJanuary 1, 2025
Swiatek had levelled the tie with a 6-3 6-4 defeat of Czechia's Karolina Muchova after Polish men's No.1 Hurkacz lost to Tomas Machac 7-5 3-6 6-4.
The pair then had to fight their way past Muchova and Machac, eventually prevailing after a tight opening set.Aiming to do better than last year's second-place finish to reigning champions Germany, Poland will face the best runners-up in Sydney in their quarter-final match.
That will be Czechia or Australia after Great Britain clinched top spot in Group F after Katie Boulter crushed Olivia Gadecki 6-2 6-1 in the opening rubber of Team GB's tie with the tournament hosts in Sydney on Wednesday night.
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