Djokovic was seeded ninth in Toronto.
Greek teenager Stefanos Tsitsipas has sent Wimbledon champion Novak Djokovic packing in the third round of the Rogers Cup in Canada with a stunning 6-3 6-7 (7-5) 6-3 win on Thursday. The Serb had seven aces and never faced a break point in the 1-hour, 25-minute match that just beat the afternoon rain.
"I thought I served well in the moments when I really need it and I was looking for the first serve", said Djokovic. Overall my game was so-and-so.
Nadal, playing for the first time since a five-set loss to Djokovic in the Wimbledon semifinals, topped France's Benoit Paire 6-2, 6-3 at night after a series of rain delays.
Greece's Stefanos Tsitsipas set up a round of 16 showdown with Djokovic by knocking off seventh-seeded Austrian Dominic Thiem 6-3 7-6 (8-6).
German second seed Alexander Zverev, the victor last week in Washington, beat American Bradley Klahn 6-4 6-4 while fourth-seeded South African Kevin Anderson edged Russia's Evgeny Donskoy 4-6 6-2 7-6 (7-0).
Rafa Nadal hits a return to Benoit Paire on his way to a routine 6-2 6-3 win that secured his place the third round.
Khachanov beat eighth-seeded John Isner of the United States 7-6 (5), 7-6 (1), and Haase topped Canadian Denis Shapovalov 7-5, 6-2.
Meanwhile, third seed Juan Martin del Potro was forced to withdraw prior to his opening match due to a left wrist injury.
"Sorry to my fans in Toronto, but I have to pull out of the tournament since my left wrist needs some days of rest", Del Potro said in a tweet.
The 32-year-old will bid for the quarter-finals here for the first time since 2015 when he plays Stan Wawrinka, who staged another fightback in three sets, beating Marton Fucsovics 1-6, 7-6 (7/2), 7-6 (12/10).
The Argentine, who looked to be in good form after reaching the final last week in Los Cabos, was replaced in the draw by Russian veteran Mikhail Youzhny.