Zhang has enjoyed a good run since the US Open, claiming the title in Guangzhou and reaching the final of the WTA 125K Series event in Ningbo, propelling her to 62nd in the rankings as a result.
The Chinese lost just three games against Nicha Lertpitaksinchai in the first round before executing a straightforward 6-2 6-2 victory over Israeli Glushko on Wednesday.
"I'm satisfied with my performance today," Zhang said. "Everything went very well and I'm happy with the result because Julia is a great player and has been doing well recently."
Zhang will face Zheng Saisai in the next round after her fellow Chinese defeated Alla Kudryavtseva 6-3 6-1.
The two have met twice in the past few months, with Zheng coming out on top in tight encounters in Suzhou and on the ITF Circuit in Sanya.
The only other players to reach the last eight were Anna Schmiedlova, who needed just 44 minutes to defeat Irina-Camelia Begu 6-0 6-0, and Anna-Lena Friedsam who was a 6-4 6-4 winner over Ajla Tomljanovic.
It was a frustrating day for second seed Yanina Wickmayer who was leading 6-2 5-2 against Wang Yafan before the match was curtailed.