Making her debut in the Wimbledon main draw, Sun fought back to topple Zheng 4-6 6-2 6-4 in just under two hours, stunning those who expected this year's Australian Open finalist to ease through her opening match.
Te Anau-born Sun switched allegiance from Switzerland in March and is the first New Zealander to make a grand slam singles main draw in seven years.
She needed to win three qualifying matches to achieve the feat, with Marina Erakovic the last Kiwi to do so when she played her 28th and final grand slam tournament in 2017.
Sun's only experience of a grand slam was a first round exit at this year's Australian Open, when she was still representing Switzerland.
She had never beaten a player in the top 50 and this result is likely to propel her world ranking of 123rd inside the top 100.
Her second round opponent will be Ukranian qualifier Yuliia Starodubtsewa, who is ranked 153rd and whose grand slam history comprises first round exits at the Australian Open and French Open this year.
Starodubtsewa advanced with a straight sets win over lowly-ranked Belgian Alison Van Uytvanck.
Sabalenka and Azarenka out
Earlier, third seed Aryna Sabalenka and 16th seed Victoria Azarenka pulled out of Wimbledon shortly before their opening matches due to shoulder injuries, leaving the women's draw short of a pair of Grand Slam champions.
Sabalenka, who was set to face American Emina Bektas, was replaced in the draw by Russian Erika Andreeva, while fellow Belarusian Azarenka's spot was taken up by another lucky loser in Frenchwoman Elsa Jacquemot.
"I tried everything to get myself ready but unfortunately my shoulder is not cooperating," Sabalenka said on Instagram.
"I pushed myself to the limit in practice today to try my best, but my team explained that playing would only make things much worse," she added.
"This tournament means so much to me and I promise I'll be back stronger than ever next year."
Sabalenka, who suffered a lower back injury this year and struggled with illness at the French Open during her quarter-final loss to 17-year-old Mirra Andreeva, suffered the injury during last month's Berlin Open.
The Australian Open champion said on Saturday that she was still not 100 percent heading into the year's third Grand Slam.
Since claiming her maiden Grand Slam title at the Australian Open in 2023, the 26-year-old Sabalenka has established herself as one of the most consistent players in major tournaments.
She reached the semi-finals at Roland Garros and Wimbledon last year, as well as the US Open final, and started 2024 by defending her Melbourne crown.
Azarenka, winner of the Australian Open in 2012 and 2013, had been set to take on Sloane Stephens.
Russian 22nd seed Ekaterina Alexandrova had earlier pulled out before her clash with Emma Raducanu due to illness.
- RNZ/Reuters