The fifth seed was made to work hard to claim the first set, with Chela racing into a 4-0 lead. However, Ferrer fought back to gain the advantage by breaking serve and taking the set 5-7.
Chela succumbed to pressure as the second set began and his Spanish opponent worked the court well to claim a 2-6 victory.
Ferrer kept up his form and finished off the Argentine with a dominant 1-6 third-set win.
The 7-5 6-2 6-1 victory sends Ferrer into the fourth round, where he will face Richard Gasquet.