The 19-year-old world number five lost the second set without winning a single game but swept to victory in the final set.
"I hope to be back next year," said Djokovic after receiving a cheque for 74,300 euros and a trophy from the hands of Portugal's former soccer great Eusebio.
"He is a great player and he deserved to win," said the 20-year-old Gasquet, who lost to Djokovic in their only previous meeting in Madrid last October.
In the women's final, Germany's Greta Arn defended two match points to become only the second qualifier to win the women's title. Arn defeat Victoria Azarenka of Belarus 2-6, 6-1, 7-6.
Pic: Djokovic receives the trophy from Portugal football great Eusebio/Getty Images.
Kohlschreiber triumphs in Munich
Local favourite Philipp Kohlschreiber landed his first ATP title by upsetting Russia third seed Mikhail Youzhny 2-6, 6-3, 6-4 in the Munich Open final on Sunday.
The unseeded Kohlschreiber, playing in his first final, looked in danger of being blown away by the more powerful Youzhny in the first set on the Munich clay but he hit back to take the second in 40 minutes and force a decider.
The 23-year-old German, who lives a few minutes down the road from Munich in Oberhaching, saved a break point in his first service game in the third set and the escape gave him a further jolt of confidence.
He played superbly to break his opponent in game five, producing a fine, deep volley to set up two break points and taking the first when Youzhny's poor attempt at a drop shot sailed into the net.
Kohlschreiber missed three match points when serving for the title at 5-4, as Youzhny sent two brutal crosscourt drives back past him before forcing an error on the German's backhand on the third.
He was handed another chance when Youzhny slightly overhit another vicious backhand across court and this time took it as the Russian's service return drifted long.
Kohlschreiber is the first German to win the Munich Open since Michael Stich in 1994.