And former world No. 3 Stan Wawrinka came back to beat 16th-seed Nick Kyrgios 1-6, 7-5, 7-5.
The four-time champion Djokovic, the ninth seed in Toronto, took care of his serve in the win over his Bosnian opponent. Djokovic had nine aces and was good on 76 percent of his first serves, converting 76 percent of his first-service points and 79 percent of his second-service points.
He had some trouble late in the second set, losing his serve to set up the tiebreak, before rallying.
The Serbian star, who last won the Rogers Cup in 2016 and is coming off a win at Wimbledon this year, will next face wild-card Peter Polansky of Canada.
Wawrinka, a three-time Grand Slam champion, came into the tournament ranked 195th in the world as he looks to get back into form following knee surgery.
The Swiss player was originally given a qualifying spot in Toronto, but advanced to the main draw when former No. 1 Andy Murray withdrew.
Kyrgios, from Australia, broke Wawrinka twice in the first-round match and had seven aces in a dominant first set.
Wawrinka battled back, converting on 86 percent of his first-service points to take the second set. He broke Kyrgios in the final game of the third set, converting his second match point opportunity when the Australian couldn't handle his return.
"Stan, for him to get through matches like this, healthy, no pain, that's a good sign for him,'' Kyrgios said. "He's playing a good level. He's got a world-class backhand and matches like this are going to give him confidence.
"But I can't take any positives away from this at all.''
Americans Sam Querrey, Frances Tiafoe and Ryan Harrison joined Russia's Karen Khachanov and Greece's Stefanos Tsitsipas as other first-round winners. Tiafoe will face Canada's Milos Raonic in the second round.
The top-ranked Canadian in the men's singles draw at No. 26, Shapovalov let out an emphatic yell when he sealed the victory in front of a cheering home crowd that included Edmonton Oilers captain Connor McDavid.
Shapovalov will play 14th-seeded Italian Fabio Fognini in the second round on Wednesday.
The Montreal native, ranked a career-high No. 133 in the world heading into the week, needed 1 hour, 18 minutes to down the No. 18 Pouille on centre court at the Aviva Centre.
"In a way he really pumped me up with his win. I was like, 'OK let's make it back to back and have two Canadians advance to the second round,'' Shapovalov said. "I'm really happy. It's a good day for Canadian tennis.''
Auger-Aliassime, on the eve of his 18th birthday, saved 5 of 6 break points and converted on 3-of-6. He also had five aces -- including four in the second set -- and won 73 percent of his first-service points.
"It's funny because I was thinking about it the whole year. I was like, 'OK, like, this year I'm turning 18. ... it's all exciting,''' Auger-Aliassime said. "I had plans for my birthday. And now that the tournament is here, it's like I have another priority.''
The teen started strong, breaking Pouille in the second game of the first set, then fighting off triple break point for a 3-0 lead.
Pouille broke the Canadian while he was serving for the set at 5-3, but Auger-Aliassime bounced back with another break for set point, letting out an approving roar as fans waved Canada flags.
Auger-Aliassime converted on another break point in the second set and held serve the rest of the way to secure just his second career win at a Masters 1000 event.
Auger-Aliassime earned his first Masters win at Indian Wells in April, defeating fellow Canadian Vasek Pospisil in the opening round to become the first player born in the 21st century to win a Masters-level match.
Auger-Aliassime lost in the qualifying round at the Rogers Cup in Toronto in 2016 and had to withdraw his wild-card entry to the 2017 tournament in Montreal with a left wrist injury.
Auger-Aliassime began the year ranked 161st.
Djokovic began his tournament a night earlier, teaming up with Wimbledon runner-up Kevin Anderson to defeat Auger-Aliassime and Shapovalov in a first-round doubles match.
"Felix, you know, he's not even 18 and playing at this stage and showing some dedication on the court and willpower, which is quite nice to see and refreshing,'' Djokovic said. "We want to see young players playing well and challenging the best players in the world."