The Chicago Bulls centre scored 40 points and collected 11 rebounds to set up a showdown with either Serbia or Lithuania, who meet in the other semi-final on Friday.
The top two teams from the 24-nation tournament will advance to next year's games in Rio de Janeiro and the next five enter three intercontinental qualifying tournaments for an extra three spots.
Spain trailed by 11 points in the third quarter but turned the tide to lead 66-63 before France forced the additional five minutes with an audacious three-pointer by Nicolas Batum.
The Charlotte Hornets guard then faltered in the final minute, showing nerves when he missed three free throws with Spain 78-75 ahead.
The effervescent Gasol, who has carried injury-hit Spain throughout the competition, put the icing on the cake with a dunk on the buzzer to silence a raucous home crowd.
Roared on by their fans in Lille's soccer stadium, which has been adapted for the event, France appeared to be in the driving seat after stifling Spain's back-court shooters.
The home side also dominated the boards in the first half, collecting a barrage of offensive rebounds as Gasol often had to battle several rivals in the paint.
But the 35-year old from Barcelona, a double NBA champion with his previous team Los Angeles Lakers, was unstoppable in attack as Spain finished off their opponents with an 8-0 run.
France's San Antonio Spurs playmaker Tony Parker looked tired and the quadruple former NBA champion was confined to 10 points after hitting only four of 17 shots from the field.
The final and the bronze medal game will be played on Sunday.
(Writing by Zoran Milosavljevic in Belgrade; Editing by Toby Davis)
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