The 36th-ranked Frenchman charged out of the blocks to take a two-set lead by dominating at the net, but the former U.S. Open champion served strongly to level.
Chardy captured the decisive break when leading 4-3 in the fifth set and calmly served out the three hour and 45 minute match, sealing it with an ace.
Chardy will next next play Andreas Seppi.
(Reporting by Ian Ransom; Editing by Patrick Johnston)
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