He will now face world number one Novak Djokovic in an attempt to reach his third consecutive Melbourne final.
"I thought it was a good match. There were a lot of good points. Most of the fun points he was winning so I was trying to keep them as short as possible," said Murray, through to his fifth consecutive grand slam semi-final.
But the 24-year-old said he had room for improvement after a poor serving display in which he was on target with only 44 per cent of his first serves.
"I need to serve better. I didn't serve particularly well but the returning was good so that was a positive," he added.