German John Degenkolb was second and Italian Matteo Trentin took third place at the end of a 187.5km ride from Besancon.
Italian Vincenzo Nibali retained the overall leader's yellow jersey after staying safe by the front of the bunch in the final descent.
Gallopin, who gave France its second stage win this year after Blel Kadri prevailed last week, powered away in the last climb and after being rejoined by Michal Kwiatkowski, Peter Sagan and Michael Rogers, he counter-attacked 2.5km from the line.
The Lotto-Belisol rider looked back several times but held off the peloton to cross the line with the bunch breathing down his neck.
"It's incredible, I want to thank my family because my father had told me that we should check up this stage, and it clearly helped," said Gallopin, who wore the yellow jersey during Monday's 10th stage.
"I would not have imagined that but I had marked that stage after coming close in Sheffield and Nancy."
Nibali's Astana team suffered a minor wobble when the Italian's lieutenant, Michele Scarponi, fell off his bike in a climb, but he finished the stage.
Ireland's Nicolas Roche was voted the most aggressive rider in the stage after trying his luck several times in the finale as the Tinkoff-Saxo team turned its focus to stage wins following Alberto Contador's exit from the race.
Roche was reined in when Sagan, who has yet to win a stage this year despite coming very close several times, led the peloton at breakneck speed in the descent towards Oyonnax.
(Reporting by Julien Pretot; Editing by Neville Dalton)
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