The American struck in the fourth game of the match and managed to take Chardy’s serve once more to close out the set.
Both players stepped up the pace on their service games in set two, not allowing each other even a single break point and taking the set into a tiebreak. The former world no.1 took a quick 5-2 lead and despite the Frenchman managed to fight back, his efforts to force a decider fell short.
Also through to the next round is German Philipp Kohlschreiber, who ousted British no.3 Jamie Baker in three sets 6-2 3-6 6-3.
The German 7th seed has been showing some fine form recently, beating world no.2 Nadal at last week’s Halle Tournament.
Kohlschreiber will play 3rd seed Andreas Seppi next, who eliminated Argentine Carlos Berlocq in straight sets 7-6 (2) 6-3.
In the other matches, Denis Istomin of Uzbekistan overcame no.2 seed Marcel Granollers of Spain, winning 6-1 4-6 7-6 (2), Belgian Steve Darcis defeated Cypriot Marcos Baghdatis 6-4 4-6 6-4 and Ryan Harrison beat Yen-Hsun Lu 6-1 7-6 (2).