Braathen, 22, was second after the first leg but produced a fine second run to win in a combined time of 1 minute 38.14 seconds in what is the third World Cup victory of his career.
"One hell of a race," said Braathen. "La Face de Bellevarde is always a challenge, it was such a tough battle.
"It was a feeling like nothing else (to win)," he added.
Austria's Manuel Feller finished second - just as he did in Saturday's giant slalom - 0.84sec in arrears and Loic Meillard was third 0.98sec adrift.
Kristoffersen's hopes of victory evaporated early in the second leg with a series of mistakes and finished down the field in sixth.
Braathen seemed surprised by his compatriot's blow-out though he always felt he had a chance of sneaking a win.
"He's (Kristoffersen) a great technical skier, on a very technical hill. But I knew it was possible to claim the victory," said Braathen.
Victory was also the perfect antidote for Braathen after Brazil's surprise elimination from the World Cup by Croatia on Friday - he is half Brazilian.
"I don't feel crying, I feel smiling," he said. "I cried enough that night. Glad I did some justice today in Val D'Isere!."
Two stars of the discipline did not even make it to the second leg.
France's Olympic champion Clement Noel and Austrian silver medallist Johannes Strolz, both straddled a gate on their first leg runs.
"I did not ski well," said Noel. "It was not how I wished it to be. I am frustated to begin the season like this."
As is his custom, runaway overall World Cup leader Marco Odermatt - winner of Saturday's giant slalom -- did not race the slalom.
