The fifth-seeded Schnyder overpowered the less experienced Liu, who was playing in only her third tour event of the season, to advance to meeting with Russia's Alisa Kleybanova in the second round.
Coming off a disappointing first-round loss at Wimbledon, Schnyder took advantage of several unforced errors by Liu, while playing an almost flawless match. She allowed only two points and won six straight games to capture the second set after falling behind 1-0.
"Right from the start I was moving great and my serve was on,'' Schnyder said. "Sometimes those matches can get tricky when you let your opponent play and (start making) mistakes, but I stayed focused the whole match. We all know how quickly things can turn.''
Liu, No. 328 in the WTA rankings, had no answer for Schnyder's two-handed backhand, which produced several winners from the baseline. A wild card entrant, Liu repeatedly hurt herself with numerous shots that went wide or into the net.
Four of the five qualifiers entered in the tournament won on Tuesday. Canadian Alexsandra Wozniak upset eighth-seeded Francesca Schiavone of Italy, 2-6, 6-3, 6-1; Michelle Larcher De Brito of Portugal beat Argentina's Gisela Dulko 7-5, 7-6 (1); Australia's Samantha Stosur defeated Anastasia Rodionova of Russia, 6-3, 6-1; and England's Anne Keothavong beat India's Sania Mirza 7-6 (4), 6-1.
Larcher De Brito, 15, is the youngest player in the tournament and will play top seed Serena Williams on Wednesday. It is Williams' first match since losing to her sister Venus in the Wimbledon finals.
The only qualifier to lose was Hungary's Melinda Czink, who was beat by Israel's Shahar Peer 7-5, 6-0.
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