The Romanian started the season well with two appearances in the last eight but has not featured in the latter stages of a tournament since the Dubai Tennis Championships, when she lost to Caroline Wozniacki.
Her 6-3 6-0 victory over Hlavackova on Wednesday sees her set up a potential quarter-final with top seed Jelena Jankovic, providing the Serb can get past Zheng Saisai.
Cirstea immediately took control of the second-round match at the WTA International hard-court event, winning the opening four games as Hlavackova struggled to settle.
Although the Czech did get on the board, Cirstea was in control and moved ahead in the match after just 35 minutes.
The second set was even easier for the world number 101 as Hlavackova was only able to win 10 points, Cirstea winning 71 per cent of the points on offer to progress to the last eight.
Fourth seed Varvara Lepchenko led the three seeds in action on Wednesday through to the quarter finals, the American beating Liu Fangzhou 7-6 (7-3) 7-5.
The world number 39 will meet Alison Riske in the next round after she saw off the challenge of Olga Govortsova 6-4 7-6 (7-3).
Ajla Tomljanovic, the eighth seed, was the final player to secure a second-round win as she cruised past Duan Ying-ying in straight sets.
The Croat's strong serve saw her win 61 per cent of points and when returning she was able to create 11 break point opportunities, Duan saved seven of those but Tomljanovic was able to do enough secure a 6-4 6-4 win.
She could now meet second seed Peng Shuai in the last eight should she come through her encounter with Israel's Shahar Peer.