Errani claimed an impressive double break to race into an early 4-0 lead. Zheng struggled to deal with Errani's movement as the Italian took the first set 6-2.
The second set began much more evenly, going by way of serve until Errani imposed her dominance once more. Zheng saw her serve broken twice and went 4-1 behind as Errani seemed to be racing away with the match.
Errani dragged Zheng around the court throughout and finally took the set 6-1 in a surpringly comfortable victory over Zheng.
The Italian now faces Petra Kvitova in the quarter-finals.