Murray insisted that he was starting to play better and seemed to enjoy having an opponent who was at their best.
"Today was the best I have played [in this tournament]," he said afterwards.
"I struggled in the last two rounds a bit and my last opponent (Gilles Simon) was struggling physically so it wasn't much of a match.
"Jeremy has beaten some great players so I had to come out sharp."
Murray, who is yet to drop a set in the tournament, is bidding to win the Australian Open for the first time.