Andy Murray beat Lorenzo Sonego 7-6 (7-3) 6-0 in a windy Toronto at the National Bank Open to reach the last 32.
Murray, who lost to Taylor Fritz last week in the second round of the Washington Open, saved two set points in the first set and fought hard to win the tie-break which was crucial to his win.
Next up for the three-time Grand Slam champion is Max Purcell on Wednesday after the Australian defeated Canada's Felix Auger-Aliassime lost 6-4 6-4.
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"It was really not pleasant to play in, really blustery, changing direction during the point," said Murray.
"We knew coming in it would feel uncomfortable. We hit on this court this morning, so I was expecting it but it still adds a bit of stress to the match and it was a really tight first set. There were lots of opportunities each way.
"I managed to sneak through the tie-break and after that he was disappointed and I relaxed a little bit."
Both players missed early break point opportunities in the first set as serve was held throughout the 88-minute opening set.
Sonego had the biggest opportunity at 5-4 and 40-15 up during the Murray serve, but failed to capitalise on the two set points and was soon punished.
The Italian won the opening two points of the tie-break, but Murray roared back and had momentum on his side.
It was much more straightforward in the second set for Murray as he completed the bagel over his opponent by not dropping a game and is through to the next round.
Norrie beaten by De Minaur; Evans dumped out
Meanwhile, British No 1 Cameron Norrie was beaten 7-5 6-4 by Alex de Minaur in one of the biggest first-round clashes in Toronto.
It was going well for Norrie when he broke in the eighth game of the first set to lead 5-3 but he missed a set point chance on his own serve and De Minaur punished him by breaking back.
Against the run of play, Australia's De Minaur won the next three games and took the opening set, before breaking early in the second.
Norrie, who also lost his first match at the Los Cabos Open last week, was unable to break back as the rest of the set went on serve so De Minaur progressed to the last 32.
Washington champion Dan Evans was stunned by Canadian Gabriel Diallo with the 21-year-old securing his first ATP Tour win with a 7-5 7-5 success.
Diallo, ranked 141st in the world, had lost all four of his previous ATP matches but rode his luck on the fifth occasion to shock Evans.
"Words cannot really describe how I feel right now. I hope that everyone in this planet can feel what I'm feeling right now, this level of happiness," Diallo said in his on-court interview. "But obviously it doesn't come without hard work behind the scenes. People don't know us as tennis players, we travel, we lose first round, we go to crazy places losing first round, it's so tough.
"But it shows that hard work eventually pays off and hopefully this can be the start of something."