The 27-year-old Bergs is set to meet Humbert again at Wimbledon in the first round.
Bergs, who had lost two finals before, ran to hug his team after sealing the win.
"The results are not there, we keep focusing on improving. And that's why we're here today, standing with the trophy," Bergs told his team during the presentation ceremony.
A timely break to go 5-3 up secured the first set for Humbert. But Bergs fought back in the second with a confident second serve, while the Frenchman made 16 unforced errors, jumping from three in the first set.
After taking the second set 6-1, Bergs continued to exploit Humbert's errors while targeting the sidelines. The strategy paid off when Humbert hit a forehand wide to send Bergs 4-3 up with a break.
Bergs held his serve to clinch victory, sealing the win when a frustrated Humbert hit the net.