Zheng triumphed 6-3 5-7 6-4 over Roberta Vinci. The match had been suspended due to the weather on Friday with the score at 6-3 5-6.
She raced into a 4-0 lead in the first set – breaking twice - and was only broken back once in claiming it.
Chinese Zheng broke immediately in the second set but the Italian broke her twice late on to take it 7-5.
Qualifier Zheng broke in the decider to go 3-1 up before seeing out the match.
“I’m just happy to win,” Zheng said. “After the rain came (on Friday), I was a little bit nervous. I really wanted to win because it was the first time I had been in the semi-finals in Birmingham.”
Ekaterina Makarova also managed to beat the rain to book her place in the last four, the Russian securing a 3-6 6-3 6-3 win over Hsieh Su-Wei of Chinese Taipei.
The other two quarter-finals were completed on Sunday.
Zheng’s last eight opponent will be Jelena Jankovic who beat Misaki Doi 6-2 6-4.
Makarova, meanwhile, faces Melanie Oudin who won the rain-delayed final set against Irina Falconi to progress 6-4 5-7 7-5.