The 29-year-old Latvian, a one-time training partner of Zverev's brother Mischa, handed the young German a lesson in perseverance and solid shot-making to reach the fourth round for the first time after 11 attempts.
"It's been a great match for me. I didn't think I could win after losing the third set and having served for the set, but he got tired and I played smarter," said Gulbis, who had only won one tour level match all year -- in the first round of the French Open -- and was ranked 138 after struggling with injuries.
"It comes from practising, playing qualifying here, getting some wins. I also qualified for Paris. It's not easy, but when you do it gives you some confidence," added Gulbis, who reached his highest ranking of 10 in 2014.
Zverev, who won a five setter against American Taylor Fritz from 2-1 down in the previous round, failed to improve on his best at Wimbledon last year when he also went out in the third round.
The 21-year-old German had the better of an even opening set that went with serve but Gulbis turned the tables in the tiebreak to take it 7-2.
Zverev came back in the next two sets but when it looked like Gulbis would not last the pace, he broke to go 4-2 up in the fourth and took the wind out of his opponent's sails.
Gulbis won the final set to love in a denouement reminiscent of Zverev's five set defeat by South Korean Hyeon Chung in the third round of the Australian Open where he also suffered a fifth-set bagel.
Zverev had suffered from a stomach bug during his match with Fritz.
(Reporting by Rex Gowar; Editing by Christian Radnedge)
