The hard-serving 23-year-old, a formidable presence on hard courts, dominated from start to finish as every facet of his aggressive game clicked, with Shelton committing just three unforced errors.
After a near-flawless opening set, Shelton fired a backhand winner down the line to break the Czech's serve for a 2-0 lead in the second, punctuating the moment with a thunderous roar.
Shelton sealed the 72-minute win in Montreal when an overwhelmed Mensik sent a backhand long on match point.
"It was a great performance, super happy with that one," Shelton told Tennis Channel.
"For me it's about building confidence. Every match I play, every practice that I have, I'm feeling better and better on these hard courts. I'm feeling more in control of the ball which allows me to go for my shots."
Defending champion Shelton will next face fellow American Learner Tien, who recovered from an early break of serve in the opening set before pulling away for an impressive 6-3 6-2 win over Spain's Daniel Merida to reach his first Masters 1000 semi-final.
Nakashima, Jodar advance
Earlier, American Brandon Nakashima and 19-year-old Spaniard Rafael Jodar also reached their first Masters 1000 semi-finals, with Nakashima beating Italy's Luciano Darderi 6-2 6-3 before Jodar defeated France's Arthur Fils 7-6 (5) 6-3.
Nakashima sent over 11 aces and offered up a subdued celebration for the career-breakthrough win in Montreal. He will meet Jodar for a place in the final after the Spaniard extended his breakthrough season with a 34th win of the year.
Nakashima, seeded 28, converted a break point in the fourth game before breaking his opponent to love to close out the first set, as the visibly frustrated Darderi's composure unravelled.
Darderi dug in his heels in the second set but could only hold off the determined Nakashima for so long, as the American broke him on the fourth try in the penultimate game.
Nakashima sent 19th-seed Darderi skittering around the court in the final game, forcing him into an error at the net on match point and pumping his fists in celebration after the customary post-match handshake.
Jodar, meanwhile, extended his remarkable first season on tour with a composed win over Fils. He earned an early break, but Fils fought back before rain suspended play again with the Frenchman serving to stay in the first set.
Jodar took the opener in the tiebreak after the restart and carried his momentum into the second set, breaking three more times to secure the victory that will lift him to at least 11th in the rankings.
The U.S. Open tune-up tournament was without several top players, including world number one Jannik Sinner and 24-times Grand Slam champion Novak Djokovic, which the Professional Tennis Players Association this week blamed on players' workload.
The men's quarter-finals began a day late after inclement weather forced the postponement of the Monday programme.