The Croatian world number 64 simply had no answer to Azarenka's power hitting as she lost 6-2 6-2.
Martic did well to carve out five chances to break serve, but the Belarus star saved all but one of them while grabbing five of the seven break points she earned.
Azarenka will face either Irina-Camelia Begu in the last four after the Romanian beat 201st-ranked American Bethanie Mattek-Sands 6-4 1-6 6-2 in what was a topsy turvy match.
Second-seeded Ana Ivanovic crashed out in shocking fashion as she was beaten 6-4 6-0 by Belgium's Kirsten Flipkens.
After a close-fought opening set, world number 12 Ivanovic crumbled in the second set as Flipkens wrapped up a win in just 64 minutes.
The Belgian will play Germany's Julia Goerges, who made it into the semi-finals with a victory over Sofia Arvidsson.
Fifth seed Goerges never looked in danger of losing the match in front of her home crowd as she used her serve brilliantly to power to a 6-1 6-4 win.
Yet though the scoreline made the match seem one-sided, Swedish world number 47 Arvidsson fought hard. She restricted Goerges to just two break points in the opening set, though lost them both times, while Goerges saved seven of the nine break points she gave up in the second set on her way to victory.
- Sports & Recreation
- Ana Ivanovic
- Kirsten Flipkens