"I think it pays off playing aggressive here in Montreal," Federer said in a courtside interview after his 6-4 6-4 win over the 12th seed.
"Plus I feel comfortable at the net so why not spend some time up there instead of slugging it out from the baseline?"
Federer opened the second set with a break and cruised through the rest of the match, which lasted just over an hour.
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With world number two Rafael Nadal eliminated on Thursday by 18-year-old Canadian Denis Shapovalov and world number one Andy Murray sidelined by a rib injury, Federer has an opportunity to regain his world number one ranking.
He would need to win the Rogers Cup and have an equal or better finish than Nadal at the Western & Southern Open in Cincinnati next week to become the world number one on Aug. 21.
"Now that Rafa is out I know I can make big strides, especially if I was to go further than the semis here. But it's all connected to great play," said the Australian Open and Wimbledon champion.
In the other quarter-finals, Shapovalov came from a set down to beat Adrian Mannarino of France 2-6 6-3 6-4, and Germany's Alexander Zverev dismissed South Africa's Kevin Anderson in straight sets, 7-5 6-4.
Earlier, Haase recovered to defeat Argentine Diego Schwartzman 4-6 6-3 6-3 in their quarter-final.
(Reporting by Rory Carroll; editing by Ken Ferris/Peter Rutherford)
