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.
Major coup for Palermo Open as Simona Halep signs up.
Chris Evert on Serena Williams’ quest for No 24.
Wimbledon to pay out £10m in prize money to the 620 players.
Katie Boulter has launched an initiative she hopes will inspire kids across the UK to pick up a tennis racket.
Wimbledon to screen immersive live show.
Remembering Goran Ivanisevic’s Wimbledon success.
Simona Halep undecided about playing at US Open.
Novak Djokovic yet to make a decision.
Andy Murray tipped to be a dark horse at US Open by Annabel Croft.
Zverev and Ferrer to link up for trial period.