WATCH the ATP Tour LIVE & ONLY on beIN SPORTS | available via Foxtel, Kayo Sports, Fetch TV & beIN SPORTS CONNECT
The third seed struck 26 winners en route to a 7-5 6-4 triumph on Thursday, but it was his serve that pleased him most.
Shapovalov, ranked 12th in the world, sent down 10 aces as Frenchman Chardy was deprived of any break-point openings.
"I've focused on my serve a lot in the past couple of weeks," the Canadian said.
"I have worked on placing it and tried out different types of serves to have more variation. I hope I can continue that.
"I've also worked on my footwork and positioning during rallies. I am feeling the ball well on both sides. If I am moving well, everything goes into place."
Harris was a surprise winner over Kei Nishikori, sealing a 6-1 3-6 6-3 success to dump out the former world number four.
Second seed Andrey Rublev defeated Marton Fucsovics 7-5 6-2 and will now face fellow Russian Aslan Karatsev.
Wildcard Karatsev continued his run with a hard-fought victory over teenager Jannik Sinner, coming from a set down in a 6-7 (5-7) 6-3 6-2 win.