In the second minute after kick-off, Rondon scored the opener with his left foot. Rondon extended the lead for Dalian in the 29th minute, as he assisted Marek Hamsik to slot home.
He doubled Flamengo's lead with a low shot that rebounded in off the post before Rodriguinho pegged a goal back for the hosts.
Valter, 22, broke free during the final few kilometers and the peloton was unable to catch him.
Spain responded with a big chance at the other end of the pitch as a misplaced return pass from Emre Can to goalkeeper Kevin Trapp allowed Rodrigo Moreno to intercept the loose ball. However, Trapp denied Moreno after blocking the shot in the nick of time in the 14th minute.
Asked whether he would be willing to return to England in the future, Bale replied, "If those options arise, it is something I'd look at for sure."
The result lifted Flamengo to fifth in the 20-team standings, five points behind leaders Internacional
PP Sports released a statement on Thursday night, claiming the termination was just a "strategic adjustment".
The women's pole vault event was also won by a Swede, as Angelica Bengtsson finished with a best jump of 4.72 meters. Enditem
The match ended in a goalless draw, despite Botafogo's 17 shots on goal to Coritiba's seven.
Duan Liuyu sent a long-distance shot off the cross-bar in the 45th minute, while Marouane Fellaini saw his header hit the post in frustration in the 61st minute. Enditem
"The final climb wasn't too hard, it was difficult to make a gap there, and therefore attacking would have been a huge effort for a small gain. So we rode steady to save energy for the coming days," Yates said.