Federer, now ranked third, won 6-3 7-6 in Saturday's first semi-final and will next play Denis Shapolov or Alexander Zverev for the trophy on Sunday.
Federer is undefeated at Grand Slam and Masters 1000 level this year.
Fourth-seeded Alexander Zverev of Germany rolled into the quarterfinals with a 6-4, 6-3 victory over 16th-seeded Nick Kyrgios of Australia, and Kevin Anderson of South Africa eliminated Sam Querrey of the United States 6-4, 6-1.
"So when I won that second set I thought let's go one more set and who knows, anything can happen". "I didn't play too well from the baseline, but Haase served better to get back into the match".
"I think it pays off playing aggressive here in Montreal", Federer said. "But Adrian did a good job of playing fast with me in the first set, really taking it to me".
All-Shapo all the time, pretty much, though Federer was careful to give Zverev equal chat time - as, indeed, Zverev was the odds-on favourite to beat the brash kid from Richmond Hill.
Magnitude 6.5 quake hits Indonesia's Sumatra island, tremors felt in Singapore
Indonesia is prone to quake as it lies on a vulnerable quake-hit zone so called "the Pacific Ring of Fire". Several Twitter users reported that they felt the tremors in Singapore.
"It's a good race and it's exciting for tennis".
"He played well", Nadal said.
Shapovalov's biggest win of his young career against the 15-time Grand Slam victor came as a result of some inspired tennis in front of a boisterous home crowd who cheered his every shot. He is Wimbledon's golden boy once again, and the tennis world has found itself reformed believers of the graceful and timeless Swiss champion. Number one for me was anyway something for later in the year. You just expect that in a finals like this. Haase has won six of his last eight semifinal matches when you include challenger play. "I just hope to take this confidence and keep going forward".
"But even Zverev, same thing".
Haase, who hit 17 winners, made a late charge and forced a second-set tiebreak before Federer stymied the challenge to win the match. Federer promptly went in for the kill, attacking the net and opening up the court to clinch victory with a deft volley.
As an 18-year-old on wild card entry to the tournament, this event was supposed to be an opportunity for him to earn experience, maybe win a match or two and perhaps get a few balls signed by one of his idols after losing to them. "Next week (in Cincinnati), different conditions, different courts, so it's tournament by tournament".
In doubles semifinals, seventh-seeded Rohan Bopanna of India and Ivan Dodig of Croatia defeated sixth-seeded Raven Klaasen of the Netherlands and Rajeev Ram of the United States 4-6, 7-6 (8), 11-9; and fifth-seeded Pierre-Hugues Herbert and Nicolas Mahut of France downed eighth-seeded Oliver Marach of Austria and Mate Pavic of Croatia 7-5, 6-3.
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