Great Britain's number one Murray fought back from a set down and a break down in the deciding set to defeat the Cypriot 7-6 2-6 6-4 in Tokyo.
"He played well under the conditions. It took me longer to find the range," Murray said. "The hardest thing for me always is changing from playing outdoors to indoors.
"It was very tough, it was very long, I did a lot of running in the first two sets.
"He is a tough guy to play against. He has a big serve. He can hurt you in many ways on the court."
Murray has won 17 out of his last 18 matches, with his only defeat in that time coming in the semi-final of the US Open against Rafael Nadal.