Chardy needed just one hour and 15 minutes to dispatch the Spaniard, who had rallied to beat Andy Roddick in the final at San Jose, California, on Sunday.
Chardy, ranked 41st in the world, fell behind in the first-set tiebreaker but rallied, then earned a break en route to a 5-2 lead in the second set.
Verdasco fended off a match point against his serve at 5-2, but couldn't hold off Chardy in the next game as the Frenchman advanced to a second-round meeting with Lukas Lacko.
"With just one day in between matches and in different conditions and not being able to practice on the stadium court before the match, it was difficult," Verdasco said. "And it was difficult for me to get the timing. But he played a great match. He served really good."
Chardy hadn't made it past the first round this year. But he didn't face a break point against the world number 11.
"It was difficult for him because he won last week and came here at the last second," Chardy said. "He couldn't practice on the courts. I knew it would be difficult for him so I started the match very aggressive."
In the women's tournament, second-seeded Melanie Oudin defeated American Alexa Glatch 6-2, 6-2.
Karolina Sprem upset fourth-seeded Lucie Hradecka 6-4, 6-4.