The Spaniard has been the most impressive of the big names so far and that remained the case yesterday as he saw off the challenge of the Croat 6-4, 6-3, 6-3.
The victory took Nadal's record on hard courts this season to 18 wins and no defeats, with only five sets dropped.
World No 38 Dodig beat Nadal 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 him on a string for much of the match, smacking 37 winners in the two-hour eight-minute victory, nearly double the number registered by Dodig, and showing his versatility by winning 14 of 17 forays to the net set up by his ferocious groundstrokes.
Nadal's countryman David Ferrer is also into the fourth round, the No 4 seed defeating qualifier Mikhail Kukushkin 6-4, 6-3, 4-6, 6-4.
Tenth seed Milos Raonic is a potential quarter-final opponent for Ferrer and he recovered from a set down to beat Spain's Feliciano Lopez 6-7 (4-7), 6-4, 6-3, 6-4.