Neither Shapovalov or Nadal could create separation during the third set that went into a tiebreak.
Nadal would have become No. 1 in the world if he had defeated Shapovalov and the victor of match between Chung Hyeon and Adrian Mannarino on Friday.
With top ranked Andy Murray out of action because of a hip injury, if Nadal manages to make it to the semis of the Canada Masters (Rogers Cup) in Montreal this week, he will be back at the top of the rankings.
While Bouchard was speaking of up-and-comers on the women's side of the draw, there is no question Shapovalov is this week carrying the torch for all Canadian tennis players - male and female - after his upset of world No. 2 Rafael Nadal in Thursday's round of 16 in Montreal.
Growing looser with each passing game, Shapovalov wrapped a couple of aces around a crackling forehand drive down the line branding a love hold for a 4-1 second-set lead.
In the second round, Shapovalov faced one of the biggest tests of his career against former US Open champions Juan Martin del Potro.
In one other upset, David Ferrer of Spain eliminated 15th-seeded Jack Sock of the United States 7-6 (4), 3-6, 6-1. "I have another week in Cincinnati, and then I have a Grand Slam coming", he said. Probably is the worst lose of the year we have, without a doubt, for me.
"I played really well in the big moments", Shapovalov said after the match.
"I also had the the opportunity I had here to come back to the No. 1".
"He has a great potential", Rafa said. With the win, Shapovalov should crack the top 100 in the rankings for the first time. next week He could go as high as No. 66 if he wins his quarter-final match against Adrian Mannarino.
Federer saw his streak of winning 32 consecutive sets end against David Ferrer but bounced back to reach the last eight.
Nadal said the match wasn't so thrilling for him. If they can play that way throughout the tournament, without Djokovic, Murray and Wawrinka there, its tough to see who can stop them.
In other results, third-seeded Dominic Thiem of Austria was upset 6-4, 6-7 (7), 7-5 by Argentina's Diego Schwartzman, and fifth-seeded Kei Nishikori of Japan, a finalist previous year, was ousted 6-7 (4), 7-6 (7), 7-5 by Gael Monfils. Earlier this week, Shapovalov started his career with a win against Brazilian Rogerio Dutra Silva.
A Polansky double fault gave Federer the break and the Swiss was soon 3-0 up after holding serve to love in the next game.
Fourth seed Alexander Zverev notched his first win over Nick Kyrgios 6-4, 6-3.
Pliskova is to move on to play sixth-seeded Caroline Wozniacki of Denmark, who defeated 10th-seeded Agnieszka Radwanska of Poland 6-3, 6-1. Poor guy. Great match!
It was the first time the Frenchman had come from a set down against a top-10 opponent in seven years.
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