It was a second stage win for the cobbled classics specialist who also won a stage last year.
Van Avermaet, 31, attacked fellow Belgian Thomas De Gendt 17.4km from the end of the 216km stage from Limoges to Le Lioran to also rip the yellow jersey from Slovak Peter Sagan.
He finished more than 2min 30sec ahead of De Gendt with Pole Rafal Majka in third over 5min back.
The overall favourites rolled in just behind Majka after an attack from the peloton by Frenchman Romain Bardet 3km from home sparked some action.
Two time former winner Alberto Contador lost more time, around 30sec, as he continues to recover from injuries sustained in crashes on the first two days.
But reigning champion Chris Froome and chief rival Nairo Quintana came over the line together.
Van Avermaet now leads Frenchman Julian Alaphilippe by 5:11 with Alejandro Valverde of Spain two seconds further back.
