The German overcame the 27th-seeded Croatian 1-6, 7-6 (7-5), 7-6 (7-1), 6-3 in 3hr 25min inside Arthur Ashe Stadium.
Zverev, seeking a maiden Grand Slam title, will play Spain’s 20th seed Pablo Carreno Busta for a place in the final. The latter tamed an erratic Canadian 12th seed Denis Shapovalov 3-6, 7-6 (7-5), 7-6 (7-4), 0-6, 6-3 in a seesaw battle to advance to his second US Open semi-final.
The 23-year-old Zverev said he stepped on the gas after finding himself a set down, and 4-2 behind in the second set.
“I just started playing maybe a little bit more aggressive because if I would have played the way I played it’s not the level for a quarter-final match of a Grand Slam,” he said.
“I just started playing better. I was a little bit more consistent and as well, my serve got better.
“I thought to myself I’m down 6-1, 4-2, I have nothing to lose at the moment,” Zverev added.
In the women’s draw, Naomi Osaka’s sharp serving and superior return game helped her past American Shelby Rogers 6-3, 6-4 and into the semi-finals, as the Japanese continues her quest for a second title at Flushing Meadows.
The 2018 champion, who was 0-3 lifetime against her opponent coming into the match, broke at love to take a 5-3 lead in the first set, where Rogers hit 16 unforced errors to Osaka’s five and held serve to claim the set.
The fourth seed broke again early in the second set for a 2-1 lead and sealed the win when Rogers dumped a forehand into the net on match point for her 28th unforced error.
“Honestly, I felt like she had the upper hand because I’d never beaten her and those memories are stuck in my head,” said the 22-year-old Osaka, who last faced Rogers in 2017.
“So, yeah, I consider this a little bit of revenge.”
She once again had tape wrapped around her left thigh but said it was just as a precaution.
Despite the loss, the 27-year-old Rogers will hold her head high after saving four match points to defeat Petra Kvitova to reach her first US Open quarter-final.
Next up for Osaka is in-form American Jennifer Brady, who beat Kazakhstan’s Yulia Putintseva in straight sets earlier in the day.
Zverev performed well when kept his first serves in play. He smashed 18 aces, while the 23-year-old Coric could only make five.
The world No. 7 struggled with consistency at times, however. He hit 12 double faults, 10 more than Coric.
His early play prompted 18-time Grand Slam singles champion Martina Navratilova to say that had played “pat-a-cake” tennis at times during his victory and he hit back later at her remark.
He bristled when he was told that Navratilova had said in TV commentary that he would never win a Grand Slam playing the way he had.
“Maybe she should look at my record against the big guys,” he said. “Maybe she should look that I’m positive against Roger (Federer). Maybe she should look at that.
“I’ve beaten Novak (Djokovic) on multiple occasions in big matches and finals. And I’m in the semi-finals, and sometimes not playing your best and finding a way is more important than playing your best.
“But she’s a Grand Slam champion, as well, multiple Grand Slam champion, she’s respected, but her opinion right now does not matter to me.”
Navratilova later clarified that her comment had been about how unaggressive Zverev, who is better known by the Russian diminutive Sasha, had been during his slow start.
“Nothing like posing a question in press conference without context,” she posted on Twitter. “I said ‘Sasha needs to play like he did in the 4th set, not the way he played the 1st 2 sets’. It’s that simple. But yeah, nice journalism, whoever asked the question. I would have answered the same way Sasha did.”
Zverev won 76 per cent of first serve points compared to just 41 per cent on his second serve.
The German hit far more winners than the Croatian though, 52 to 37.
It was a close contest, with Zverev accumulating 136 points in total, just four more than Coric.
The disqualification of top seed Novak Djokovic on Sunday blew the men’s competition at Flushing Meadows wide open.
His departure means the US Open will crown a first-time Grand Slam winner on Sunday.
In Wednesday’s quarter-final matches, second seed Dominic Thiem plays Australia’s Alex de Minaur and third seed Daniil Medvedev takes on Russian compatriot Andrey Rublev.