Larsen is a retired Danish badminton player who won major international singles titles in the 1990s, and ranks among Denmark's badminton greats.
At Rio de Janeiro's Olympic stadium, former Chelsea forward Salomon Kalou made his debut for Botafogo but could not inspire the hosts to victory over Coritiba.
The victory sends Garcia into the third round, equaling her best US Open result after finishing at that stage every year from 2016 to 2018.
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.
Before the game, Dalian ranked seventh with six points in the eight-team division in northeastern China's Dalian city, while Henan, also on six points, sat at the bottom by virtue of their inferior goal difference.
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.
The result lifted Flamengo to fifth in the 20-team standings, five points behind leaders Internacional
Valter, 22, broke free during the final few kilometers and the peloton was unable to catch him.
He doubled Flamengo's lead with a low shot that rebounded in off the post before Rodriguinho pegged a goal back for the hosts.
The hosts added their third goal when Daniel Sampaio latched onto Marco Antonio's pass to slot home in stoppage time.
"So you have to make her in trouble. That's what I like and it was a great challenge for me today. I did well in this challenge and I can take the happiness for it, and now I'm after another one."