Djokovic, seeded ninth, cruised past Canadian wild-card entrant Peter Polansky 6-3, 6-4 for a second-round victory in 1 hour, 25 minutes.
The 31-year-old Serb, who earned his 13th career Grand Slam last month, won 83 percent of his first-serve points and never faced a break point.
"I thought I served well in the moments when I really need it and I was looking for the first serve," Djokovic said. "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-so). In the moments when I probably needed to step it up, I did."
Polansky said of Djokovic, "He raises his level on the big moments. I only got one free point on a 30-all or deuce. ... But what I found trickiest out there was just his serve locations. He doesn't have the biggest serve, but he's putting every serve on the line, or an inch from the line, every time."
Earlier Wednesday, Del Potro tweeted, "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's exit gave a first-round bye to Russia's Mikhail Youzhny, who hadn't advanced through qualifying after withdrawing on Sunday. Youzhny's stay in the main draw didn't last long, though, as the Netherlands' Robin Haase beat him 7-5, 6-2 in a second-round match.
Russia's Karen Khachanov upset 12th-seeded Pablo Carreno Busta of Spain 6-4, 7-6 (3). Belarus' Ilya Ivashka got past American Ryan Harrison 7-6 (5), 6-4 in a battle of qualifiers.
Top-seeded Rafael Nadal of Spain, who fell to Djokovic in the Wimbledon semifinals, and second-seeded Alexander Zverev of Germany, who won the Citi Open in Washington last week, were scheduled to play their second-round matches Wednesday night.
--Field Level Media