Nadal, whose incredible run on clay came to an end when he was dumped out of the Madrid Masters by Dominic Thiem, has responded well to that disappointing defeat and he is yet to drop a set in Italy.
He and Shapovalov exchanged service games in the opening set until the seventh game when Nadal found the break.
ATP World Tour Masters 1000 - Italian Open - Foro Italico, Rome, Italy - May 17, 2018 Spain's Rafael Nadal celebrates during his third round match against Canada's Denis Shapovalov
Image credit: Reuters
Shapovalov was clearly rattled after that and he was broken in the opening game of the second set as he finished the match with six double faults.
Nadal took total control after that and he now will face Fabio Fognini in the next round.
"It was a solid match for me," Nadal said. "I started with some mistakes on the return but with my serve, I didn't lose many points."
Former world number one Novak Djokovic is also in the quarter-finals for the first time this year.
Djokovic, back after a troublesome elbow injury, showed flashes of his formidable best as he beat Spain's Albert Ramos-Vinolas 6-1 7-5 and will meet Japan's Kei Nishikori in the next round.
Nishikori, who like Djokovic is trying to come back from injury, was in complete control against Philipp Kohlschreiber, defeating the German 6-1 6-2.