Fourth-seeded Zverev, coming off a win last week in Washington, D.C., and seeking a fifth tournament win this year, will face Swiss legend Roger Federer in the final on Sunday.
And the decider was one-way traffic for Federer, who saw out the win with a textbook serve and volley to set up a last-eight meeting with Roberto Bautista-Agut.
The youngster responded impressively to Nadal easing through the first set to force a decider, where Shapovalov saved three break points before winning an epic 14-minute third game, which included 10 deuces.
Federer is 17-0 in his career against the 35-year-old Ferrer, who was ranked third in the world in 2013 but is now at No.33.
Quarterfinals: At Montreal: Robin Haase bt Diego Schwartzman 4-6, 6-3, 6-3; Roger Federer bt Roberto Bautista-Agut 6-4, 6-4; Denis Shapovalov bt Adrian Mannarino 2-6, 6-3, 6-4; Alexander Zverev bt Kevin Anderson 7-5, 6-4. I played in five finals this year.
The 36-year-old Federer has his longest winning streak since 2012.More news: Tesla CEO Elon Musk fires back at "bogus" assistant story on Twitter
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"If I don't save those match points in the first match, there's no chance of being here". At just 18 years, Shapovalov became the youngest player ever to reach the round 16 of a Master Series since Rafael achieved the feat in 2004 at Miami. "Plus I feel comfortable at the net so why not spend some time up there instead of slugging it out from the baseline?"
Next up is Roger Federer who served his way into his 6th final of the season besting Robin Haase 6-3, 7-6 (5). The 18-year-old left-hander from Richmond Hill, Ontario beat France's Adrian Mannarino 2-6, 6-3, 6-4 and awaits the victor of the late match between fourth-seeded Alexander Zverev of Germany and Kevin Anderson of South Africa. "Roger plays very fast and he didn't want to rally with me, so he went for his shots". I don't know about myself either.
It must be said that Bautista Agut, 12th favorite in Montreal, is a player particularly strong this season. This will be the first match on hard court.
For nearly two decades, spectators have flocked to Federer's breathtaking matches and followed the ebb and flow of his career. "I was more committed and a step further in, adjusting my position slightly realizing the ball does fly a lot".
A win will give help Federer reach his first final of the tournament since losing to Jo-Wilfried Tsonga in 2014 title match. "I started off pretty slow, just drained from (Thursday)". "It drains you because you know you can do better, but actually your own body is not letting you".