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.”
The veteran tennis champion's comfortable win comes after a closely-fought encounter with Spain's David Ferrer in the previous round.
Federer advances to the semi-finals where he will face Robin Haase of the Netherlands, who defeated Diego Schwartzman 4-6, 6-3, 6-3 earlier in the day.
Bautista Agut struggled on his serve as he was broken three times and won just 65 percent of his first serve points.
“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 an ATP Tour high five titles in 2017.
He will face Dutchman Haas in just the second career meeting between the two.
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's win over Mannarino came just 24 hours after he defeated 10-time French Open champion Nadal to get into the quarters. Shapovalov also upset former US Open winner Juan Martin Del Potro in the second round.
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