Kyrgios produced his career highlight by knocking Rafael Nadal out of Wimbledon earlier in the summer but he was unable to dent Murray’s challenge in the Canadian city.
Murray dominated the match with his serve, producing seven aces in the two sets to book a clash with Richard Gasquet in the next round.
It was Murray’s first match since failing to defend his Wimbledon title with a last-eight exit from the All England Club last month.
The 27-year-old British No 1 is on a Rogers Cup quarter-final collision course with Novak Djokovic should he progress in his debut hardcourt tournament of the season. The event offers his main preparation before the US Open begins on 25 August.
“Kyrgios has obviously got a lot of confidence with the way Wimbledon went and winning his first match here but I played with a lot of variety, which has always been my game really,” Murray said after the match. “I maybe went away from that a little bit at some points over the last year or so but that’s when I play my best tennis and it worked well today.”
Earlier, Roger Federer launched his North American hard court campaign and bid for an 80th career title in impressive style, blowing past Canadian Peter Polansky 6-2, 6-0 and into the third round
The women’s version of the Rogers Cup in Montreal lost power both figuratively and literally with hometown favourite Eugenie Bouchard suffering a second-round defeat by American qualifier Shelby Rogers. The 20-year-old Bouchard, playing for the first time since losing in the Wimbledon final to Petra Kvitova last month, faltered badly in front of her home crowd. Her 6-0, 2-6, 6-0 loss came after the event suffered a seven-hour power cut that shut down scoreboards and umpires’ microphones.
“I was feeling the pressure on the court and I was feeling kind of match rusty,” Bouchard said. “But I knew this coming into the match, so I can’t use that as excuses. I knew it would be kind of a difficult situation.”
Bouchard struggled with her serve from the outset and failed to claim a game in the opener. She rebounded to dominate the second set but fell away badly in the decider, ending home fans’ hopes of a quarter-final showdown against top-ranked Serena Williams.
The in-form Bouchard is the only player to have reached the semi-finals of the first three grand slams of the season while defending champion Serena has won this tournament three times.
Serena had the day off but her older sister Venus fought her way to a three-set victory against Anastasia Pavlyuchenkova 6-1, 3-6, 6-2.
“It was like going back to the southern California juniors,” Venus said of the power outages. “But I tried to think of it as positive. It felt good to win the match and hopefully gain some momentum.”
In other matches, Caroline Wozniacki made easy work of Daniel Hantuchova in a 6-1, 6-1 triumph, while third-seed Agnieszka Radwanska defeated Barbora Zahlavova-Strycova 6-4, 6-4 and ninth-seed Ana Ivanovic routed Timea Bacsinszky 6-1, 6-2.