After trading sets, Gasquet trailed 4-3 in the decider but broke back to 4-4 in a game that went to seven deuces with Kukushkin constantly failing on his forehand shots.
Gasquet served at love to go 5-4 ahead and converted his first match point when Kukushkin's forehand cross sailed wide.
With the victory, Gasquet overtakes fellow Frenchman Jo-Wilfried Tsonga in the quest for the eighth spot in the season-ending ATP Tour Final in London next month.
It was Gasquet's third title of the season.
Kukushkin was playing in his first final since winning his only title in St. Petersburg in 2010. He was only the second qualifier to reach the final here since Paul-Henry Mathieu won the title in 2002.
The 18th-ranked Halep has dropped only one set in four final appearances since winning her maiden title in Nurnberg, Germany, in June. Halep constantly trapped Stosur in the corners and beat the 2011 U.S. Open champion with precise crosses and shots down the line.
Stosur, who lost the 2012 final here, saved 11 break points in the first set before Halep dominated the tiebreaker. The fifth-seeded Halep jumped to a 4-1 lead in the second and sealed the victory with a break on her first match point, when the seventh-seeded Stosur netted her return.
"It's an incredible year for me and I enjoy every moment of it," Halep said.
With the victory, Halep is projected to rise to a career high 15th in the WTA Tour rankings on Monday.
Stosur, who hadn't dropped a set in her last six matches before Sunday, was looking to win back-to-back titles after winning the fifth crown of her career in Osaka, Japan, last Sunday.