Despite being 5-4 and a break down during the opening set, world number 34 Dimitrov rallied to win the contest 7-6 6-1.
"I was just trying to hang into the match. It's never easy playing against Janko. Today was one of these days I was really looking forward to coming out on court and actually having a lot of fun, just trying to play good tennis in a way," he told reporters.
"I fought till the last point in the first set. I gave an extra edge as the match went on. I was very happy with the performance today."