It was a meeting of two of the most unorthodox players on tour and a rematch of their classic Australian Open clash in 2012.
That was Tomic's only win in six previous meetings against the Ukrainian but he won the big points on Thursday to secure a 6-4 6-3 victory.
Tomic said on atpworldtour.com: "He's very difficult to play. I knew as soon as I was playing him it was going to be a difficult match. I don't like playing him. I played the right tennis. I was very focused and very clear what I needed to do."
The 21-year-old next plays qualifier Sergiy Stakhovsky, a 6-4 6-3 winner over Australian wild card Marinko Matosevic.
This is Stakhovsky's best week since his sensational second-round upset of Roger Federer at Wimbledon last year.
Top seed Juan Martin del Potro has a tough battle with veteran Radek Stepanek but came through 6-4 3-6 6-3 and will play fourth seed Dmitry Tursunov, who beat Denis Istomin.
In the women's event, Bulgaria's Tsvetana Pironkova became the first qualifier to reach the final in the event's history with an upset win over second seed Petra Kvitova.
Pironkova has had the most success on grass during her career and took advantage of the fast courts to win 6-4 6-3 and make her first WTA Tour final.
The 26-year-old said on wtatennis.com: "It's definitely a milestone. This is something I've been dreaming about for a long time now and something that I've been missing - to get to a final or even win a title."
In the final Pironkova will face fifth seed Angelique Kerber, who used her experience to beat American teenager Madison Keys 6-4 6-2.