The No.5-seeded Peng broke serve twice in each set and saved all three of the break points she faced throughout the match to beat wildcard Liu, 61 63. She broke at love in the last game of the match.
"She played really well today," Peng said of her opponent. "She's taller than me and she served well. We come from the same city, but I've never played her before, so the first few games were tight.
"Also, although it's technically still 2013, this was the first match of the new season and I was very nervous. It had been a long time since I played a match. I had been training all winter. Eventually I was able to settle in and in terms of strategy and rhythm, I think I played pretty well in the match."
At No.42 in the world, Peng is China's No.2 player. China's No.1 player is Li Na, the World No.3.
Anna-Lena Friedsam, Viktorija Golubic, Risa Ozaki and Lyudmyla Kichenok secured berths in the main draw with wins in the final round of qualifying. They will all play their first round matches on Monday.
Elsewhere the doubles draw kicked off, with all four seeded teams taking the courts. Chinese rising star Zhang Shuai was among those in action, seeded No.1 with countrywoman Zheng Saisai - they cruised.
"I'm happy to have such a good match to start 2014," Zhang said of their 76(6) 62 win over Annika Beck and Donna Vekic. "Although we fell behind early in the first set, we were patient and came back."
Not so lucky was Vera Zvonareva, who - in her first match of any kind since the London Olympics - fell in doubles. She and Olga Govortsova lost to Johanna Konta and Patricia Mayr-Achleitner, 61 26 108.