Toronto, Canada – World number 14 Cilic needed an hour and 13 minutes to quell his 104th-ranked opponent.
"I think I played a pretty good match. Most important my service was very good," Cilic told reporters.
Big-serving Cilic breezed through the opening set after breaking Kunitsyn in the third and fifth games and quickly led 3-1 in the second.
"I think he didn't have any breakpoints in the match which shows that I was top of him, especially in the first set," said Cilic, who beat Indian Somdev Devvarman in last year's final.
"In the second I got an early break and I was able to control from there."
(Reporting by Sanjay Rajan; Editing by Ed Osmond)