The two players could not be separated for much of the opening set, but a double fault by Murray while serving at 6-5 down helped the world number one clinch the set, before going on to win the match 7-5 6-2.
The Serb told Sky Sports News: "We have played so many times. We know what to expect. It will be physical with long exchanges and whoever is calmer in the important moments and comes up with the big shots can prevail.
"He was a break up in the second, but he made some mistakes, made some double faults and allowed me back in. Then I was swinging through and I felt better.
"I don't think the physical factor played an advantage for me too much, but I think maybe winning the first set gave me an edge."