Gasquet struggled in the first set but was on a roll at the end, breaking the Russian veteran's serve three times in the third set and grabbing a 3-6, 7-6 (7-4), 6-3 triumph.
"He was playing fast in the first set," Gasquet said afterward. "I just tried to keep focused and to fight a lot, and I did it."
Gasquet improved to 8-10 lifetime in title matches.
Davydenko was playing in his third Qatar final in four years. He won the event in 2010 and was runner-up in 2011. He conceded he felt fatigue in his legs by the time the third set began.