Baghdatis, who burst on to the world stage when he made the Australian Open final in 2006, regained his composure after a lapse in concentration to claim his fourth ATP title in the final lead-up event before the first grand slam of 2010.
The 24-year-old made a flying start at the Sydney Olympic tennis centre, breaking Gasquet's opening service game then taking the first set, but lost his way after a 75-minute delay early in the second set.
Gasquet quickly established a 5-2 lead and served for the set but Baghdatis broke back and eventually sealed victory in the tiebreak.
"I felt pretty good on court," Baghdatis said.
"I've just won a tournament, confidence is up, feeling pretty fit. I think everything is positive.
"I have some things to work on stillÂ…my serve, first serve percentage. I think that's all. It's the only thing that worries me a bit," he added
Baghdatis has been plagued with injuries over the past two seasons and was reduced to playing on the Challenger circuit last year.
He won three Challenger titles and an ATP event in Stockholm and has been in great form this week, advancing to the final after tough three-set wins over Lleyton Hewitt and Mardy Fish.
He is drawn to play Italian Paolo Lorenzi in his opening match at the Australian Open, which begins on Monday.
"Next week, if I stay focussed and find the way to win the first two, three matches, then I could be very dangerous and confident," Baghdatis said.
Gasquet, who faces Russian Mikhail Youzhny in the first round at Melbourne Park, missed two grand slams last year after he became involved in a doping case.
The 23-year-old was provisionally suspended in May after testing positive for cocaine but was later cleared of any wrongdoing after explaining that he became contaminated from kissing a woman in a nightclub.
"I'm disappointed, because it's always difficult to lose a final," he said.
"I served a bad game (in the second set), and I had a big trouble in the tiebreak. I lost a lot of free points, so that made the difference."
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