Federer hammered five aces, made just two double faults and won 81 percent of his first serve points in the 68-minute centre court match. He dominated at the net, winning 21 of 25 points.
"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.
"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 struggled on his serve as he was broken three times and won just 65 percent of his first serve points.
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"Today, I felt that I didn't get into the rhythm of the match and I didn't feel the ball well," he said. "Roger plays very fast and he didn't want to rally with me, so he went for his shots."
Federer posted his seventh consecutive win over the Spaniard and improved his season record to 34-2. He has a ATP Tour high five titles in 2017.
The pair met in a Davis Cup World Group play-off in 2012 with Federer winning 6-1, 6-4, 6-4.
Federer's chances of winning another title this season were given a boost when top seed Rafael Nadal was upset by world No. 143 Denis Shapovalov of Canada on Thursday night.
Shapovalov, who needed a wild card to gain entry into the tournament, continued his cinderella run Friday by rallying to beat Frenchman Adrian Mannarino 2-6, 6-3, 6-4.
Mannarino became the fourth established ATP player this week to fall at the hands of the 18-year-old lefthanded Canadian.
Shapovalov started slowly by dropping the first set before settling into the match in the second. After a rain delay, Shapovalov broke Mannarino to take a 4-2 lead in the second set. Her served out the set in the ninth game.
"It's tough to come out and serve after a 12-minute rain delay. I knew that was a very big turning point," Shapovalov said. "When I broke him I got that little bit of confidence, and I started believing in my shots again."
Haase has had to overcome several injuries in his career but says he is finally in a good place.
"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.
"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."
Zverev, 20, is the youngest player ranked in the top 20 in the world and Shapovalov is the youngest since 1990 to reach a Masters 1000 quarter-final.
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