AG2R La Mondiale rider Geniez held firm as an early 18-rider breakaway was whittled down to sprint home ahead of Team Sky’s Dylan van Baarle and Mark Padun of Bahrain-Merida.
Spain’s Jesus Herrada did enough to grab the lead in the overall classification with an advantage of three minutes and 22 seconds over the now second-placed Yates.
Herrada had been part of the initial breakaway but fell away to finish just over two minutes behind the leading pack, with the peloton which included Yates almost 12 minutes back.
Geniez’s win was marred when he swerved to avoid photographers and crashed into a race official shortly after crossing the finish line, bringing down a number of other riders including Van Baarle.
The 181km stage saw a series of attacks from the start until a prominent bunch including the likes of Geniez, Van Baarle and Vincenzo Nibali managed to establish an advantage of over 10 minutes.
A further attack split the leading group but Geniez and Dylan Teuns (BMC) were among those to haul them in, while Herrada hung in in his bid to claim the red jersey.
Despite sporadically losing touch with the leaders, Geniez and Van Baarle worked themselves back into contention and set up the final sprint in which the Frenchman stole a march on his rivals.
Herrada will take his advantage into the forthcoming stages in the Asturias and Leon mountains, while Spanish veteran Alejandro Valverde (Movistar) remains one second behind Yates in third place.
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