The Spaniard was in dominant form as he controlled from start to finish against his Dutch opponent.
A break in the seventh game of the first set was enough to secure the first stanza, and Ferrer opened the second set with a break before securing that set 6-3.
Ferrer then cantered to victory in the third to move into the next round.
"Today he was all over the court. He was just hitting his shots, you know, penetrating every volley, low slice, serving really good. He always serves good," said Dimitrov.
"I just couldn't find the rhythm, and I couldn't achieve any of the little opportunities that I had in the match."
France's Richard Gasquet, seeded 12, won 6-2 6-1 7-5 against Austria's Bernard Tomic while former world No. 1 Lleyton Hewitt, who had reached two quarter-finals in 13 visits before Tuesday, lost 3-6 6-2 6-1 6-4 to Argentine Carlos Berlocq.
Tommy Haas, the 16th seed, pulled out with an injured shoulder when leading 5-2 in the first set against Juergen Zopp of Estonia.
Nicolas Almagro of Spain, the 21st seed, also withdrew, with an injured foot, from his match against Jack Sock of the U.S. when trailing 5-0 in the first set.
French Open men's singles first round results
Ivo Karlovic (Croatia) beat 11-Grigor Dimitrov (Bulgaria) 6-4 7-5 7-6(4)
19-Kevin Anderson (South Africa) beat Stephane Robert (France) 7-5 6-3 6-4
28-Philipp Kohlschreiber (Germany) beat Pere Riba (Spain) 7-5 6-4 6-1
32-Andreas Seppi (Italy) beat Santiago Giraldo (Colombia) 6-3 7-5 6-3
Juan Monaco (Argentina) beat Lucas Pouille (France) 6-3 6-1 6-4
Axel Michon (France) beat Bradley Klahn (U.S.) 6-1 6-7(4) 5-7 6-1 6-4
Carlos Berlocq (Argentina) beat Lleyton Hewitt (Australia) 3-6 6-2 6-1 6-4
- Sports & Recreation
- Grigor Dimitrov
- Lleyton Hewitt
- Ivo Karlovic