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 the 6-1, 7-6 (2) victory.
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.
Brazil are currently eighth in the FIFA women's world rankings, behind the US, Germany, France, Netherlands, Sweden, England and Australia. Enditem
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.
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
Arrascaeta restored his team's two-goal advantage with a diving header in heavy rain but Jose Pimentel responded with his side's second goal just before halftime.
The 28-year-old is now 16th in the overall rankings, 16 seconds behind new leader Yates.
Earlier, sixth seed Petra Kvitova of the Czech Republic edged past Ukraine's Kateryna Kozlova 7-6 (3), 6-2, and eighth seed Petra Martic of Croatia beat fellow Ukrainian Kateryna Bondarenko 6-3, 6-4 to also advance into third round. Enditem
Lurie took charge of the Eagles in 1994, and led the team to its first Super Bowl title in 2017.
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.
With the win, Suning leapfrogged Luneng into second place on the table with 17 points from nine games, two points adrift of Fabio Cannavaro's Guangzhou Evergrande who have played one match less.