For Nadal, it was the ideal response after his surprise defeat to Austria's world No 8 Dominic Thiem in the Madrid Open quarter-finals that also saw the Spaniard lose his No 1 ranking.
Nadal routed 31st-ranked Damir Dzumhur 6-1, 6-0, while Djokovic beat Georgian qualifier Nikoloz Basilashvili 6-4, 6-2.
It is the 13th time in his career Nadal has dropped only one game in a match, but he is still looking for his first "double bagel".
"I played very well today", said Thiem, who beat Rafael Nadal in the Madrid Open semifinals last week. And that's what I did today.
With AP Photos.Fabio Fognini got the Foro Italico crowd fired up with a 6-4, 1-6, 6-3 win over sixth-seeded Dominic Thiem in the second round of the Italian Open.
"For some reason, I couldn't get a ball in the court after that, on my backhand side", Osaka said. "I did have chances", said Thiem. So I'm disappointed that I lost, obviously.
Also on the red clay, Kei Nishikori rallied to beat third-seeded Grigor Dimitrov 6-7 (4), 7-5, 6-4.
Pliskova racket rage Former world number one Karolina Pliskova was so angry she put a hole in the umpire's chair with her racket instead of shaking hands after losing to Greece's Maria Sakkari.
The controversial shot came in the third set with the Czech serving at 5-5 (30/30).
Earlier, top women's seed Simona Halep needed just under an hour to advance 6-1, 6-0 past Naomi Osaka to avenge her defeat to the Japanese player in Indian Wells.
Shapovalov reached the third round of the Italian Open on Wednesday with a 7-6 (3), 6-7 (5), 6-3 win over Dutch veteran Robin Haase. The chair umpire acknowledged that she "lost" the ball mark and therefore said the point should be awarded to Sakkari. "That was the way that I want to play".
Halep needed to save four break points in her opening service game for 1-1 but then reeled off 12 in a row.
"I don't know how many mistakes I made, but not many".
Halep reached the final in Rome a year ago and needs to reach the quarter-finals this time to retain her world number one ranking.
Also, U.S. Open champion Sloane Stephens held off a comeback from Estonian qualifier Kaia Kanepi in a 6-0, 5-7, 6-4 victory; seventh-seeded Caroline Garcia defeated Timea Babos 6-3, 6-4; and 14th-seeded Daria Kasatkina eliminated American qualifier Danielle Collins 6-2, 6-3.
Fognini's victory was far less straightforward, but the 30-year-old eventually prevailed 6-4 1-6 6-3 against last year's semi-finalist.