Suzhou, who had scored only three goals in their previous five matches, took an early lead as Li Zhi converted a penalty in the 16th minute.
Baena, the world number 101, battled to a 7-5, 6-7, 6-3, 3-6, 8-6 victory to reach the third round of a Grand Slam for the first time in his career.
FC Barcelona has had an excellent start to the campaign and has looked much sharper and stronger under Ronald Koeman's guidance in their opening two matches. However, it will be without central defender Clement Lenglet on Sunday, with the Frenchman missing the match against his former club Sevilla after being sent off in Vigo on Thursday. Enditem
The Slovak will face Argentinian qualifier and world No. 131 Nadia Podoroska for a spot in the round of 16.
Pedro latched onto Giorgian De Arrascaeta's cross to fire in a shot from close-range, just two minutes after Patrick de Paula had put his team ahead with a thumping 20-yard effort.
World No. 1 and top seed Novak Djokovic will kick off his campaign for an 18th major title against Sweden's Mikael Ymer later on the central court. Enditem
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"Especially here in Paris, I'm extremely happy because it's my favorite Grand Slam and favorite tournament of the year. I always play good here. I had many chances in last couple of years. I had match points or really close matches. I always play good here, just didn't close it," Schmiedlova said after the victory.
"I will be competing for the first time since running under two hours at the INEOS 1:59 Challenge. I'm happy to race with the dominant athletes, that is how the sport is and should be treated like that. Competition makes the sport beautiful," he added.
"To make things easier I told the players yesterday [Wednesday] that this was the right way to go," he added, suggesting the decision was of his own volition.
Ye's teammate Yu Yiting won the title in the final in 4:42.12s, Zhang Yifan from Hebei, got the silver and Yin Jiahe, also from Zhejiang, took third place.