The second-seeded Spaniard has lost just 21 games through three matches. He has faced only five break points, saving each one of them.
"I am winning because I am playing well from the baseline and I am making the right decisions in the right moments," Nadal said.
The 38th-ranked Dodig beat Nadal at the hard-court tournament in Montreal two years ago. But Nadal is looking like the king of hard courts these days, with an 18-match winning streak on the surface.
He closed out the victory with a service winner to win the last game at love.
Nadal will next face 22nd-seeded Philipp Kohlschreiber, who beat the top American man, John Isner, at this stage for the second straight year. Isner's 6-4, 3-6, 7-5, 7-6 (5) loss means the host country has only one player left in the men's draw. Tim Smyczek, ranked 109th, plays his third-round match against 43rd-ranked Marcel Granollers on Sunday.
Isner lost despite 26 aces and plenty of home-crowd support, unlike in his previous match.
After beating France's Gael Monfils in the second round, Isner said he was "disappointed" that fans were cheering so vociferously for Monfils. On Saturday, there were chants of "U-S-A! U-S-A!" in the second set, and "Here we go, John! Here we go!" in the fourth set -- but Isner failed once again to figure out Kohlschreiber.
"I felt like I wore myself out getting charged up out there," said Isner who at one point pointed his right index finger toward the Louis Armstrong Stadium stands and circled his arm overhead, riling up the fans. Two points later, sprinting so far he nearly reached the seats, Isner hit a forehand that closed a point, punched the air and then shook his fists, doing his best Jimmy Connors imitation.
"I used too much energy, and I shouldn't have done that. It was stupid on my part. So I was pretty gassed there. Had I kept it calm, I think I could still be out there right now."
Roger Federer moved into the fourth round at the US Open for the 13th year in a row, racing through a 6-3, 6-0, 6-2 victory over 63rd-ranked Adrian Mannarino in only 1 hour, 21 minutes Saturday night. The 17-time major champion compiled a 34-8 edge in winners.
Through three matches, Federer has spent 4½ hours on court, dropping a total of only 21 games. Federer, who won five consecutive US Opens from 2004-08, next plays 19th-seeded Tommy Robredo of Spain, who ended the run of 179th-ranked qualifier Daniel Evans of Britain 7-6 (6), 6-1, 4-6, 7-5.
"You come to New York, and if you're not excited anymore, you're in the wrong place. ... You don't like the sport the way you should," Federer said. "If you don't put in 100 percent effort here or in other places that really you care about, then something's wrong with you. ... I'm just totally excited being here. I have always enjoyed playing here. Have never had a bad tournament at the US Open."
Also Saturday, fourth-seeded David Ferrer needed nearly three hours to down 172nd-ranked qualifier Mikhail Kukushkin 6-4, 6-3, 4-6, 6-4. His next opponent is No. 18-seeded Janko Tipsarevic, who also took four sets to knock off 20-year-old American Jack Sock 3-6, 7-6 (1), 6-1, 6-2.
Raonic, the highest-ranked man in Canada's history, does not need to worry about the same kind of expectations that players such as Isner do.
"The relief, definitely, is there is obviously a lot more pressure on Americans," Raonic said. "I'm sort of doing a lot of stuff into unchartered territories, so people are very supportive of it, whereas I feel it's a little bit unfair to the American players. Everybody is expecting Pete (Sampras) and (Andre) Agassi to be there on the top."
Information from The Associated Press was used in this report.