Federer rolled to a 6-4, 6-4 victory over the Spaniard to move closer to winning his sixth ATP title of the season.
Federer, who is 34-2 this year, will meet Dutchman Robin Haase in the semis. Haase outlasted Argentina's Diego Schwartzman 4-6, 6-3, 6-3 in his quarterfinal match.
Federer controlled the action at the net, winning 21 of 25 points, while cruising past Bautista Agut.
"It pays off playing aggressively here in Montreal, plus I feel comfortable at net, so why not spend some time there instead of slugging it out from the baseline," Federer said in a post-match television interview. "I think I did a good job again, even though it was tough to control the ball. I got some decent rhythm going."
Bautista Agut battled Federer closely in the first set before the Swiss picked up at the pace to win it. Federer held the edge in the second set but Bautista Agut was able to hold his head high despite the outcome.
"I wanted to play a great tournament, and I think I did have a good week," Bautista Agut told reporters. "Today, I felt that I didn't get into the rhythm of the match and I didn't feel the ball well. Roger plays very fast and he didn't want to rally with me, so he went for his shots.
"To be in the quarterfinals here in Montreal is a very good result for me, also getting hard-court matches under my belt."
Federer will be facing Haase for the first time since a 2012 Davis Cup match.
Haase improved to 5-0 all-time against Schwartzman with his comeback after losing the opening set.
He also reminisced on his career, saying he finally is back in his comfort zone after being mentally drained by injuries that derailed his career.
"I wasn't the player I was before my injury," Haase said. "I was not as fast. I was insecure. I had a lot of problems with other injuries after. Then this kind of eats you up inside mentally. It drains you because you know you can do better, but actually your own body is not letting you. That took me, honestly, a couple of years to get more calm in my head, that I have to deal with it.
"I've been working on it a lot in the past few years. I started to believe more and more again. My game is better. Then I started this year winning back-to-back matches against really good players. Then you're thinking, 'OK, it might happen again.' That it happens, it's just awesome."
Schwartzman was dejected after being outplayed in the final two sets.
"The week for me was very good, but I am now disappointed as I don't think I played well in the second and third sets," Schwartzman said afterward. "I didn't play too well from the baseline, but Haase served better to get back into the match."