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.
There were also second round wins for fourth seed Stefanos Tsitsipas of Greece, fifth seed Alexander Zverev of Germany and seventh seed David Goffin of Belgium.
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 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 31-year-old's poor relationship with Real Madrid coach Zinedine Zidane is well documented and was made clear when Zidane only used him in two of the 12 games his side played when Spanish football resumed in June after lockdown.
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.
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 hosts added their third goal when Daniel Sampaio latched onto Marco Antonio's pass to slot home in stoppage time.
"I was looking to take the jersey on stage six anyway so I'll go in with the same tactic - try to win the stage and see what happens."
Jumbo Team's Van Aert produced a powerful sprint in the slight uphill finish to win by half a wheel ahead of Cees Bol and Sam Bennett.