Suarez said he was ready for the clashes against Chile in Montevideo on October 8 and Ecuador in Quito five days later.
The French champions will kick off the continental campaign at home against Manchester United on October 20.
The South American zone's 2022 World Cup qualifiers had been scheduled to begin in late March but were postponed because of the coronavirus pandemic. Enditem
"I think I played a really good match. I was very aggressive. I knew from last year I had to change something, so I really wanted to be better than last year and definitely, I was today," said the world No. 2.
Thanks to the third-round win, Wuhan moved atop the championship group standings with six points.
"In the second set and the third set, I had a lot of opportunities, also easy opportunities," said Schwartzman after his 20th victory of 2020. "That's why I was really upset, really angry with myself at that time ... when I was close to winning in those sets. I couldn't do it."
Jiangsu played a more aggressive game in Tuesday's faceoff with Shanghai, which had led the championship group before the third round. In the 70th minute, Wu Chengshu received a pass from the left side and rifled an effort into the net, helping Jiangsu gain a 1-0 lead.
However, the six-time Ballon d'Or winner has not been able to win a major trophy at international level; a gold medal at the Beijing 2008 Olympics notwithstanding. The 2022 World Cup in Qatar might be his last chance to change that.
Leeds United and Manchester City producing a thrilling 1-1 draw which lived up to expectations in terms of entertainment and suspect defending.
In other games in Chengdu, after a goalless first half, Beijing Renhe broke the deadlock in the 57th minute to claim a 2-0 victory over Suzhou Dongwu. Taizhou Yuanda defeated Inner Mongolia Zhongyou 2-0.
Xinjiang registered a balanced stat sheet in offense with five players scoring in the double figures, led by Han Xu's 13 points and 10 rebounds.