Fils will aim for his second title of the year in Tuesday's final, while Humbert, who beat Czech Republic's Tomas Machac 6-3, 3-6, 6-2 in the first semi-final earlier in the day, will look to win his third hardcourt trophy this year.
A close line call did not go Fils' way when he had a set point in the first tiebreak, with Rune winning the replayed point to make it 6-6.
But Fils held his nerve and won the set with a light-touch backhand that left a frustrated Rune slamming his racket onto the court.
Fils broke early in the second set to take a 2-0 lead, but world number 14 Rune broke back in the next game and almost led 4-3 before Fils saved a break point to stay even as the second set went to a tiebreak as well.
The world number 24 Fils took a 6-3 lead, but Denmark's Rune saved five match points in the seesawing battle before Fils finally took victory with a precisely timed forehand, reaching the fourth ATP final of his career.
Fils' opponent in the final, world number 19 Humbert, bounced back from a second-set stumble against Machac earlier, controlling the third set with a superior first serve, hitting four aces and winning 13 of his 14 first serve points.
Paris Olympics mixed doubles gold medallist Machac was unable to score a single point in his last two service games, with Humbert converting a match point with a strong forehand.
Humbert, who has won all six of his finals on the ATP tour, beat Fils in all their previous meetings, including twice this year.