Zheng, who won the WTA Tour's Zhengzhou Open in October, swept past her seventh-ranked opponent 6-1, 2-6, 6-1 in Perth.
"It was just a normal match for me," said Zheng, the WTA's 2023 Most Improved Player who has risen to be world number 15.
"It doesn't matter who I face. I'm happy with the win and excited for my team."
It followed teammate Zhang Zhizhen defeating Jiri Lehecka 5-7, 6-3, 6-4 in China's maiden appearance at the mixed teams tournament.
Zhang held his nerve against Lehecka in a heavy-hitting clash, with the world number 58 dictating from the baseline.
"I'm so happy I controlled my emotions well after losing the first set," he said.
Zheng and Zhizhen would then go on to win the mixed doubles match 6-1, 6-2, completing a clean sweep for China.
Ruud, the top-ranked Norwegian in history after reaching a career-high two by making the 2022 US Open final, was a level above Tallon Griekspoor in a 6-3, 6-4 win at Sydney.
He converted three of seven break points to clinch victory in 72 minutes against a player who has risen to 23 in the world on the back of ATP Tour titles in Pune and Hertogenbosch this year.
It helped level the tie at the mixed teams tournament after experienced Dutchwoman Arantxa Rus downed Malene Helgo 7-6(4), 6-1 in the women's singles.
Ruud, now ranked 11, returned to partner Ulrikke Eikeri in the mixed doubles, but they were unable to overcome Demi Schuurs and Wesley Koolhof who rallied from a break down in each set to win 7-6(5), 7-5.
"I think we just returned pretty well, we just found a way to break their game," said Schuurs.
Despite losing the tie, Ruud said his singles win was "the perfect start to the season".
"I really like this court, it was a good match for me," said Ruud, who lost to Novak Djokovic in this year's French Open final.
"I'm ready for the new season, I'm motivated, I have a lot of energy in my legs."
Rus, who at 33 became the oldest first-time WTA title winner in 40 years when she won in Hamburg last season, gave the Netherlands the perfect start.
She broke Helgo immediately before the young Norwegian forced a tiebreaker.
The second set proved easier, with Rus rattling through despite Helgo putting up late resistance to save four match points.
Alexander Zverev and three-time Grand Slam winner Angelique Kerber get their tournament underway later in Sydney when Germany take on Italy.
World number one Iga Swiatek spearheads the Polish team in Perth when they face Brazil.
