"I think I'm just playing more freely overall and with more confidence because I can get to more balls without thinking," Federer said after the match.
The Swiss superstar converted his first break point against Dolgopolov late in the first set and then closed out the set with an ace.
In the second set, Federer seized control of the match on Dolgopolov's serve as the two battled over seven deuces points, with Federer finally converting the break chance.
"I think it's nice winning anyway. It just solves a lot of problems and makes you feel better, you know, happier," Federer said.
Federer, the No. 7 seed, has yet to drop a set in the tournament. He is currently on an 11 match winning streak and is now 19-2 on the season. Last year's health problems are quickly becoming a fading memory.
"I think the results are better than I thought they would be," Federer said. "I expected myself to play better starting March/April, sort of this time around ... So for it to all start earlier gives me more information how my body is, how my mind is, and from now on I really feel I am really there where I want to be or where I wanted to be six months ago."
Federer will re-enter the Top 5 with his BNP Paribas Open performance and will look to capture a 22nd ATP World Tour Masters 1000 title Sunday.