Briton Geraint Thomas kept the leader’s yellow jersey.
Julian Alaphilippe of France was the fastest in the climb but he made his move just too late and finished six seconds behind, just ahead of Stuyven.
Team Sky stays at the top of the leader board with Thomas finishing ahead of his nearest rivals team mate Chris Froome and Sunweb’s Tom Dumoulin.
Sunday’s 15th stage is a 181-km hilly ride to Carcassonne ahead of the second rest day.
After that, three stages in the Pyrenees that could shake up the overall standings.
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