Robson defeated Cirstea in the semi-finals 12 months ago, but the Romanian failed to overcome her first hurdle this year when she was well beaten by Serbia's Bojana Jovanovski 6-2, 6-1.
Robson, seeded third this time, eased through to the second round with victory over Serbian Jovana Jaksic 6-2, 6-4 in her opening game.
Robson will next play home hope Zheng Saisai, who won a gruelling 6-7 (3/7), 6-3, 7-5 tie against Thailand's Luksika Kumkhum which lasted two hours 50 minutes.
Also through to the next round were the second seed Alize Cornet of France, who outclassed Olga Govortsova of Belarus 6-3, 6-1, and the Chinese pair of Zheng Jie and Peng Shuai.
In Tuesday's other first-round matches, Austrian Yvonne Meusburger beat Ukraine's Lesia Tsurenko 6-3, 6-4, and Serbian Vesna Dolonc overcame Poland's Urszula Radwanska 7-5, 6-2 in a hard-fought game which lasted almost one hour 50 minutes.
Current champion Hsieh Su-Wei of Taiwan sailed through her first-round match on Monday.
Results from the Guangzhou Open WTA tennis tournament in Guangzhou, China, on Tuesday (x denotes seedings):
Bojana Jovanovski (SRB) bt Sorana Cirstea (ROM x1) 6-2, 6-1
Yvonne Meusburger (AUT) bt Lesia Tsurenko (UKR) 6-3, 6-4
Vesna Dolonc (SRB) bt Urszula Radwanska (POL x5) 7-5, 6-2
Laura Robson (GBR x3) bt Jovana Jaksic (SRB) 6-2, 6-4
Zheng Saisai (CHN) bt Luksika Kumkhum (THA) 6-7 (3/7), 6-3, 7-5
Zheng Jie (CHN) bt Yaroslava Shvedova (KAZ) 6-1, 6-4
Timea Babos (HUN) bt Varvara Lepchenko (USA x7) 7-6 (10/8), 7-5
Peng Shuai (CHN x4) bt Shahar Peer (ISR) 6-3, 6-4
Alize Cornet (FRA x2) bt Olga Govortsova (BLR) 6-3, 6-1