The Great British number one started slowly in Tokyo and lost the opening set 6-3.
However, he fought back to win the next two sets, only affording his Spanish opponent four points during the third and decisive set.
"I played some great tennis and the third set was some of the best I've played against him," said Murray.
"There were a lot of close games towards the end of the first set and beginning of the second and I managed to get the momentum and didn't give him many chances after that.
"I was very consistent, didn't make too many mistakes and kept a cool head in the important moments."
The victory marked Murray's second title success in seven days, having won the Thailand Open last Sunday.