The hosts added their third goal when Daniel Sampaio latched onto Marco Antonio's pass to slot home in stoppage time.
Members of the US women's team filed a lawsuit against their federation in March because of alleged discrimination over wages. A federal judge ruled against the players, who have since lodged an appeal.
Fourth seed Naomi Osaka of Japan booked her place in the third round with a comfortable 6-1, 6-2 win over Italy's Camila Giorgi.
The 28-year-old is now 16th in the overall rankings, 16 seconds behind new leader Yates.
The 54-year-old Dane announced he has been receiving medical treatment for the condition after being diagnosed some years ago and, with the assistance of doctors, has continued to carry out his duties as BWF president "without limitation," said the world governing body.
He doubled Flamengo's lead with a low shot that rebounded in off the post before Rodriguinho pegged a goal back for the hosts.
Garcia looked untouchable in the first set and for much of the second, blasting 30 winners and breaking Pliskova's serve three times en route to a 6-1, 7-6 (2) victory.
Rondon continued to demonstrate his prowess in the second half. In the 48th minute, the Venezuelan striker assisted Swedish winger Sam Larsson to stretch the lead for Dalian.
A product of the Ajax youth academy, Van de Beek made his first-team debut in 2015. In total, he played 175 official matches for Ajax, scoring 41 times.
With this result, Dalian are sixth in Group A with nine points, while Henan with six points remained in last place. Enditem
Caboclo added that national women's team manager Pia Sundhage was informed of the decision in March.