"I think I played well all the match,'' Chardy said. "It was tough but I play very well in the tiebreakers.''
Chardy, who lost his first career tour final to fellow Frenchman Jo-Wilfried Tsonga in Johannesburg earlier this month, initially held a 5-2 lead in the first set.
But Baghdatis forced a tiebreaker. At 7-7, Baghdatis double-faulted and smacked a backhand wide to surrender the set.
Baghdatis erred early on in the second-set tiebreaker. He netted a forehand to fall behind 3-2 then netted a backhand to give Chardy his first match point at 6-2.
Playing in his second quarterfinal of the season, Baghdatis saved the first match point with an ace.
Chardy took control of the second match point on his own serve with a forehand volley that forced Baghdatis into another error.
Chardy will face the winner of the Friday night match between top-seeded Mardy Fish and sixth-seeded Florent Serra.
In the other completed quarterfinal match, Christophe Rochus beat 2000 Delray Beach champion Stefan Koubek 6-3, 7-6 (6).
"I'm really happy because I've never beaten him before,'' Rochus said. "I lost four times. He has the kind of game I don't like to play.
"But I'm playing really good for the moment.''
Koubek struggled with his serve. Rochus broke him in the second and fourth games to secure the first set, but fell behind 5-2 in the second set before rebounding.
In the semifinals, Rochus will play the winner of the match between qualifier Evgeny Korolev and Guillermo Garcia-Lopez.
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