There looked nothing wrong with Kyrgios's serving arm as he banged down 20 aces on the grass and he delighted fans with a trademark tick shot which proved a turning point in the decider.
With Marterer serving at 2-3 Kyrgios played a shot through his legs for a winner and it appeared to ruffle Marterer who then made two unforced errors to drop serve.
Kyrgios then held his next two service games to book a clash with Spanish left-hander Feliciano Lopez.
Lopez, runner-up last year before going on to win the Queen's Club title, beat Frenchman Gilles Simon 7-6(6) 6-4.
"This is very important for me, to have weeks on grass. It's a very unique surface. You play only two, three weeks a year ... it's so important to get matches, to get hours on the grass and (you get more) when you win," he said.
Top seed Roger Federer will be back in action on Friday when he plays Guido Pella.
(Reporting by Martyn Herman; Editing by Alison Williams)
