The world number four lost the first set 7-6, but recovered to record a 7-6 6-1 6-1 victory.
The opening set proved to be an even contest, with neither player able to break each other's service game. The resultant tie-breaker was not as close, though, and Dodig was able to win through 7-3.
A tie-breaker was also required in the second set but on this occasion Ferrer edged through 8-6.
That appeared to hamper world number 49 Dodig, who failed to cope with Ferrer's speed across the court thereafter. He was only able to pick up just two more games as the Spaniard sealed his slot in the last eight.