"We played well with counterattacks. We had several chances to score. Krzysztof Piatek had the best chance but Jasper Cillessen saved it," added the 49-year-old.
The win puts Kenin into the third round at the US Open for the fourth year in a row. The American has come up short against top players like Maria Sharapova (2017), Karolina Pliskova (2018) and Madison Keys (2019) at this stage in the past.
There were also third round wins for Belgian star Elise Mertens, Belarussian veteran Victoria Azarenka and France's Alize Cornet.
38-year-old Williams closed out the first set with ease but had trouble in the second when she was broken twice by Gasparyan.
Liu was victorious in the 2019 Women's World Cup, defeating 2017 winner Zhu in last year's final.
In the women's doubles, Xu Yifan from China and America's Nicole Melichar reached the second round after edging past their opponents in straight sets. Enditem
The 2020 CBSL runs from August 27 to September 14 in Chengdu. Due to the impact of the COVID-19 pandemic, all games are played behind closed doors. Enditem
Ancelotti, 61, signed a four-and-a-half-year deal with Everton last December after having been sacked by Italian Serie A side Napoli earlier that month. He led Everton to finish 12th in the Premier League last season. Enditem
This year, world number four Kenin counts herself among the top players, but the challenge won't get any easier as Tunisia's Ons Jabeur, one of the most in-form players of 2020, awaits in the next round.
In an earlier match, Shenzhen edged defending champion Zhejiang 3-2, with both teams of similar strength showing their best from the very beginning.
The disappointing results and performances in the country's first two games after a 10-month long break caused by the COVID-19 pandemic might have provided evidence of how difficult it is to propel Germany forward.