Both players traded serves in the opening set before Murray broke to go into a 5-3 lead. He served out the next game to claim the first set 6-3.
Murray instantly broke his Australian opponent in the second set, before wrapping up the match 6-3 6-2.
"He started very well but I managed to get into a lot of long rallies at the end of the first set and got through," said Murray.
"I'm just moving so much better. It's such a huge part of my game, so when I move well the rest of my game goes well and it made it hard for Bernard to hit lots of clean winners."
The Scot will face third seed Alexandr Dolgopolov in tomorrow's final.