World number two Nadal, seeking a fifth Rogers Cup title, started slowly before dispatching the Italian 2-6 6-1 6-2.
Also advancing to a last-eight meeting were France's Gael Monfils, who beat Poland's Hubert Hurkacz 6-4, 6-0, and Spanish 10th seed Roberto Bautista Agut, who dispatched Frenchman Richard Gasquet 7-5, 7-5. "If I had the chance to have the legs that I had in that 2005, probably would be a very, very good player, no?"
Coming off a victory on clay in Austria for his third title of the year, Thiem will face eighth-seeded Daniil Medvedev of Russian Federation, a 6-3, 6-3 victor over Cristian Garin of Chile.
She broke again for a 2-1 lead in the second and never looked like surrendering the advantage. Of course, I'm so confident coming here. Playing in his first action since losing to Roger Federer at Wimbledon last month, the 33-year-old Spaniard enjoyed an easier outing than his opening match against England's Daniel Evans on Wednesday when he rallied from a tiebreak deficit.
"Everybody knows he's one of the big talents on tour", said Nadal, who lost to Fognini in the third round of the 2015 U.S. Open.
"Let's see tomorrow. Another opportunity to be in another final". In the victory, Fognini won 65 percent of his first serve points and 53 percent of his second serve points. It's true that during his career he had some up and downs.
Hero's welcome for deceased Vietnam War veteran
According to Knight's obituary, he served as a typing clerk in the Philippines, Japan and Korea before becoming a fighter pilot. He was initially declared Missing in Action until being declared Killed in Action seven years later.
Earlier on Friday, the eighth-seeded Medvedev needed just under 57 minutes to finish off Thiem, the No. 2 seed from Austria.
He will face compatriot Karen Khachanov, who rushed past 2017 champion Zverev 6-3 6-3. "It saved me a lot of energy".
"With all the traveling and short transition, two very tough matches yesterday and two days ago, I think the battery was empty today", said Thiem who won Kitzbuhel on Sunday.
Third seed Alexander Zverev of Germany will face Khachanov in the quarters after a 7-5, 5-7, 7-6 (5) win over Georgia's Nikoloz Basilashvili.
Khachanov beat Medvedev in Moscow last fall.
"He's having a great season already winning a Masters 1000 and playing some great matches all around".