The Spaniard has been the most impressive of the big names so far and that was no different on Saturday as he saw off the challenge of Croatian Dodig 6-4 6-3 6-3.
That took Nadal's record on hard courts this season to 18 wins and no defeats, with only five sets dropped.
The second seed said: "I think I played a correct match today [Saturday]. I'm happy with the score against a player who came to this tournament winning against tough opponents like (Nikolay) Davydenko and (Fernando) Verdasco.
"To be able to win against him in straight sets is great news. I played better today [Saturday] than in the previous matches, which is always a positive thing.
"Tomorrow [Sunday] I have another day for practice and to be better for the match on Monday. So that's all. It's an important win for me. Every win means a lot. I'm happy the way that I am playing, and I'll try to be ready for the next one."
Dodig had beaten the Spaniard before, in Montreal two years ago, and he gave it everything, requiring treatment to his left leg in the first set after tumbling in an effort to reach a Nadal passing shot.
But Nadal had the Croatian on a string for much of the match and, although the games were close, early breaks in each set proved more than enough for the second seed to progress.
Nadal is yet to have his serve broken this tournament but he believes that is more to do with how he is playing off the ground.
He said: "In important moments I did a few good serves, but I am winning because I am playing well from the baseline and I am making the right decisions in the right moments.
"It's something I am going to work a little bit more on tomorrow. I need to serve a little bit better."
Next up for Nadal will be a last-16 meeting with German Philipp Kohlschreiber, who defeated top American hope John Isner 6-4 3-6 7-5 7-6 (7/5).
It was a repeat of a match here at the same stage last year, which Kohlschreiber won in five sets after 2am.
Fourth seed David Ferrer has not been in great form, and he was not entirely convincing today in defeating qualifier Mikhail Kukushkin 6-4 6-3 4-6 6-4.
He will next play 18th seed Janko Tipsarevic, another man struggling for form, who fought back from a set down to beat American Jack Sock 3-6 7-6 (7/1) 6-1 6-2.
Tenth seed Milos Raonic also came from behind to beat Spain's Feliciano Lopez 6-7 (4/7) 6-4 6-3 6-4 and set up an intriguing fourth-round clash with eighth seed Richard Gasquet, who was two sets to one up when Dmitry Tursunov retired.