The Katusha team rider led a breakaway pack of cyclists that overtook two breakaway riders with only around 50 meters left of the race to win in thrilling style.
Australian Heinrich Haussler was second, and Peter Sagan of Slovakia took third-place.
Kristoff's second win over the last four stages was over a flat 222km course from Tallard, southeast France’s towards Nimes. The Norwegian also won stage 12, a more arduous 185.5km route, from Bourg-en-Bresse to Saint-Etienne.
Vincenzo Nibali finished to keep the overall lead. He is 4 minutes, 37 seconds ahead of Spain’s Alejandro Valverde in second, and 4 minutes, 50 seconds ahead of France’s Romain Bardet in third.
Monday is the riders' second rest day of the competition.