Djokovic, who is coming into the tournament on the back of winning his 13th Grand Slam title at Wimbledon last month, was untroubled by Canadian wild card Peter Polansky.
“I thought I served well in the moments when I really need it,” Djokovic said following the 6-3 6-4 win.
“I thought I found pretty good accuracy and angles with the first serve and also my second serve worked pretty well.
“Overall, my game was so-and-so. In the moments when I probably needed to step it up, I did.”
Nadal, meanwhile, who was playing his first ATP Tour match since losing to Djokovic in the Wimbledon semi-final, bulldozed his way past Frenchman Benoit Paire 6-2 6-3, and he will now face Stan Wawrinka in the next round.
— Tennis365 (@T365Official) August 7, 2018
“I don’t play a singles match on hard court since Australia,” said Nadal. “So is a long time. And that’s it. You need time.
“And the victories of course helps and good to work on the practice for sure, no?
“But even if you have a good work on the practice, you need matches to get that percentage that you need.”
“I feel that of course I was not at my 100 percent today. But at the same time it’s true that it’s impossible.
“After a while, you need matches. And when I say I don’t feel myself 100 percent, I say that I didn’t play fantastic match, but I didn’t play a bad match, no?”
Elsewhere, Washington Open winner Alexander Zverev was too good for Bradley Klahn, but fourth-seed Kevin Anderson needed three sets to get past Evgeny Donksoy.
John Isner was also successful, but Fabio Fognini couldn’t transition his fine claycourt form onto hardcourts, losing to Denis Shapovalov.
Seventh seed and Roland Garros finalist Dominic Thiem was knocked out by up-and-coming Greek player Stefanos Tsitsipas 6-3, 7-6.
In other Rogers Cup news, Juan Martin del Potro has been forced to withdraw with a wrist injury.
Dubai Duty Free Tennis Championship draw revealed.
Juan Martin del Potro won’t be heading to Acapulco.
Juan Martin del Potro out, Dan Evans still in.
Felix Auger-Aliassime into his maiden ATP Tour semi-final.
David Goffin up next for Stefanos Tsitsipas.
Frenchman brands crowd ‘sheep’.
Czech to face Bencic for the title.
Could a new era be dawning?
Prospects seem to have brightened for Brit.
Australian making wrong kind of headlines again.