The 11th-seeded American, who reached the semi-finals last week in Washington, could only laugh out loud on match point as Bublik raced to reach a drop shot.
Knowing he would be unable to get there in time, the colourful Kazakh skilfully tossed his racquet under the dropping ball on the run before it landed, causing a reverse drop shot back over the net into Shelton's court.
The maneuver was, of course, illegal, with Shelton winning the match with a huge smile after 89 minutes with nine aces among his 27 winners. Bublik finished with the same number of unforced errors.
"It was crazy, but a special shot regardless," the 21-year-old American said. "I asked after the match and the point doesn't count if the racquet leaves your hand before it touches the ball.
"But it shows the skills he can do. This was a funny moment on match point that we shared -- he's the only guy who could do something like that."
Shelton said waiting for his chances was key on the day: "It was important that I stayed patient throughout. He's a guy who gets back a lot of balls."
Shelton earned his 27th win of the season as he reached the second round on his second appearance in Canada.
The American had lost two previous matches with Bublik, both played on clay at Masters 1000s in Rome and last spring in Madrid.
Olympic doubles bronze medalist Tommy Paul made a quick turnaround from Paris, posting a 6-4, 7-6 (7/2) win over Luciano Darderi.
The American had defeated the Italian in the Olympic first round before losing a quarter-final to Carlos Alcaraz.
"I was pumped to get through the first round," the winner said.
Paul has been on a roll this summer, winning Queen's Club before reaching quarter-finals at Wimbledon and the Olympics.
The 10th seed said conditions were totally different from last week in Paris, where the clay courts seemed slower.
He said balls in Montreal fly like "little rubber rockets -- they are really coming off the racquet."
Britain's Jack Draper was upended at the first hurdle in a 7-5, 6-2 loss to Jordan Thompson, the Australian winner moved into a match against second seed Alexander Zverev.
Elsewhere, there were first-round victories for France's Ugo Humbert, Croat Borna Coric and Australian Rinky Hijikata.
