The Norwegian, 22, led after the first run by 0.41sec and clocked a combined time of 1min 43.31sec to finish 0.15sec ahead of five-time overall champion Marcel Hirscher of Austria.
Germany's Felix Neureuther claimed third, at 0.63sec.
Hirscher consolidated his current lead atop the overall standings, having amassed 973 points, 281 ahead of Kristoffersen (692).
Kristoffersen, who also won here last year, added victory in Wengen to his wins in Adelboden, Val d'Isère and Madonna di Campiglio this season, and takes the lead in the slalom standings 20 points ahead of Hirscher.
"Things are going pretty well at the moment," he said. "So I am happy about that."
Hirscher said it was good to get back racing after winter storms forced the cancellation of Saturday's downhill."
"Picking up 80 more points is a pretty good result. You can't always win," he said.