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.
Kyle Edmund’s improbable attempt to plot a path to the ATP World Tour Finals has taken a few interesting twists.
ATP and ITF trying to figure out best way forward for the Davis Cup, says Novak Djokovic.
Simona Halep ‘very proud’ of year-end No 1 achievement.
Our betting expert Derek Bilton is hoping to nail down a third straight winning week.
In Tennis Today, Novak Djokovic is a man of many talents.
Juan Martin del Potro is set to miss the rest of the 2018 season after picking up a serious knee injury.
Take our 10-question teaser on the career of Martina Navratilova.
Novak Djokovic defeated Borna Coric to win the Shanghai Masters title.
Caroline Garcia beat Karolina Pliskova in the Tianjin Open final.
Dayana Yastremska dispatched Wang Qiang in the Hong Kong Open final to win her first WTA Tour trophy.