The Canadian dropped just eight points on serve in eight service games en route to a 6-4, 6-0 win over the World No. 73 Slovak in just 52 minutes. The lefty was a perfect six-for-six on net approaches.
It was a strong response from the 22-year-old, who last week suffered an upset straight-sets defeat to fast-rising Czech Jiri Lehecka in Rotterdam.
Shapovalov improved to 8-3 on the season, having started the year by leading Canada to victory at ATP Cup and by reaching the Australian Open quarter-finals, where he pushed eventual champion Rafael Nadal to five sets.
In the quarter-finals, Shapovalov, who had a first-round bye, will meet Frenchman Arthur Rinderknech, who enjoyed a 6-7(5), 6-1, 6-4 win over seventh-seeded Kazah Alexander Bublik, who has now suffered two first-round defeats following his first tour-level title in Montpellier.
Rinderknech kept Bublik under pressure on serve throughout the match, earning 18 break point chances and converting six times, while dropping serve three times himself.