Djokovic, the world number one, was flawless in a 6-1 6-2 demolition of French seventh seed Richard Gasquet while Nadal was equally emphatic in a straight sets win over Australian qualifier Marinko Matosevic.
Serbia’s Djokovic and Spaniard Nadal will face off for the 36th time after the 11th seed Milos Raonic and local wildcard Vasek Pospisil compete in an all-Canadian semi-final.
Djokovic was imperious against Gasquet as he produced his best performance since returning from a month off after losing the Wimbledon final.
Unleashing his full repertoire of big serves, crushing ground strokes and plenty of touch, Djokovic barely raised a sweat as Gasquet was emphatically dispatched in just 52 minutes.
The crowd then got more entertainment when Djokovic returned to the centre court for what has become his customary celebration dance as the stadium roared its approval.
“It’s a great feeling when you’re playing this well and you beat a quality player like Gasquet,” Djokovic told reporters.
“I’m going to try to memorise what I’ve done today and how I felt and hopefully take it on the court tomorrow … same kind of feeling.”
Nadal was always in control of his quarter-final against a fatigued Matosevic, who had come through two qualifying matches on top of his three main draw victories.
The 12-time grand slam champion never looked like being seriously challenged under the lights and he let rip with a procession of thundering forehand winners on the way to a 6-2 6-4 victory which booked his place in another Masters series semi-final against Djokovic.
“It is always exciting to play against Novak in a great tournament, a Masters 1000,” Nadal said in a courtside interview. “It will be a great match and I’ll try my best as I always do.”
Local favourite Milos Raonic held his nerve to beat Latvia’s Ernests Gulbis in a thrilling quarter-final to join fellow Canadian Vasek Pospisil in the semi-finals.
Raonic, the world number 13, kept his cool in front of a parochial home crowd as he overcame Gulbis 7-6(3) 4-6 6-4 in a two and a half hour showdown.
With the crowd willing him on and jeering Gulbis’ every shot, Raonic claimed the first set tiebreak, before his opponent forced a deciding third set through a brilliant display of shot making.
Gulbis kept swinging in the decider but Raonic’s serve got him out of some difficult spots and when his opponent wobbled, Raonic pounced to seal victory and set up a meeting with Pospisil.
“It’s a great thing, it means a lot, not just to us but to Canadian tennis,” Raonic said.
“But at the same time, it’s another tennis match. That doesn’t change.”
Pospisil won through after Russia’s former world number three Nikolay Davydenko, who had showed signs this week of a return to form, retired while trailling 3-0 in the first set of their quarter-final.
The 71st ranked Pospisil had already beaten American John Isner and Czech fifth seed Tomas Berdych this week in three sets so was happy to finally have a lighter workout.
“Even in those three games, I was really trying to catch my breath,” a tired Pospisil said.
“I felt like I had a bit of sore legs … so it (quick win) came at a great time.”
Andy Murray’s singles campaign may have ended prematurely but the Wimbledon champion and partner Colin Fleming have won through to the doubles semi-finals.
They defeated the fifth seeded Aisam Ul-Haq Qureshi and Jean-Julien Rojer to set up a match against the top ranked Mike and Bob Bryan.
(Editing by Julian Linden/Greg Stutchbury)