The hosts added their third goal when Daniel Sampaio latched onto Marco Antonio's pass to slot home in stoppage time.
In the 48th minute, the Venezuelan striker assisted Swedish winger Sam Larsson to stretch the lead for Dalian.
But things didn't go as organisers may have expected.
Garcia now faces No. 28 seed Jennifer Brady of the United States as she looks to reach the round of 16 for the first time. Enditem
The result lifted Flamengo to fifth in the 20-team standings, five points behind leaders Internacional
"I rode my tempo and gave it all to create a gap big enough to win."
Klein called safeguarding the club's financial pattern more important than ever for the future of football.
"Our development will not be redirected. It is just a strategic adjustment based on reality. We will continue to hand the best services to our fans and partners," it added. Enditem
Brazil are currently eighth in the FIFA women's world rankings, behind the US, Germany, France, Netherlands, Sweden, England and Australia. Enditem
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
In other matches on Wednesday, Ceara beat local rivals Fortaleza 1-0, Atletico Goianiense drew 1-1 at Fluminense, Corinthians won 2-1 at Goias and Bragantino drew 1-1 at Athletico Paranaense. Enditem