Last year's runner-up Ferrer of Spain, the fifth seed, bulldozed his way into the last 32 by demolishing Italian Bolelli in 108 minutes.
The fifth seed, who could take on eight-times champion Rafa Nadal in the quarter-finals, will next play Argentine Juan Monaco or Italian 32nd seed Andreas Seppi.
"I am ready for the next round and was very happy with my performance, especially with my consistency," he said.
"My season on clay has been good (when asked about beating Nadal on clay this season). I have a good feel but I'm focusing on the moment."
Croatian 16th seed Ivo Karlovic reached the third round with a 7-5 6-3 6-4 win over Andreas Haider-Maurer.
"I have actually never won a match outside of the U.S. on red clay. So to win two here at the French Open, it means a lot," Young said.
Spain's Guillermo Garcia-Lopez followed up nicely on his first-round defeat of third seed Wawrinka by beating France's Adrian Mannarino 6-4 6-3 4-6 6-0.
Round 2 results:
Leonardo Mayer (Argentina) beat Teymuraz Gabashvili (Russia) 6-2 4-6 6-4 6-4
Guillermo Garcia-Lopez (Spain) beat Adrian Mannarino (France) 6-4 6-3 4-6 6-0
Dusan Lajovic (Serbia) beat Juergen Zopp (Estonia) 6-2 6-4 6-4
1-Rafa Nadal (Spain) beat Dominic Thiem (Austria) 6-2 6-2 6-3
19-Kevin Anderson (South Africa) beat Axel Michon (France) 6-2 6-3 6-2
Donald Young (U.S.) beat 26-Feliciano Lopez (Spain) 6-3 7-6(1) 6-3
5-David Ferrer (Spain) beat Simone Bolelli (Italy) 6-2 6-3 6-2
Ivo Karlovic (Croatia) beat Andreas Haider-Maurer (Austria) 7-5 6-3 6-4
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- Sports & Recreation
- Rafa Nadal
- Ivo Karlovic