The Cofidis rider sped away from a skimmed pack on a steep slope some 2.5 km from the line and never looked back.
His compatriot Dani Moreno (Katusha) was second and Dutchman Wilco Kelderman (Belkin) took third place, both two seconds off the pace.
Spaniard Alberto Contador (Tinkoff-Saxo) retained the overall leader's red jersey after finishing seventh with the other top contenders, five seconds behind Navarro.
Former Giro d'Italia champion Damiano Cunego and multiple Tour de France stage winner Luis Leon Sanchez of Spain were in the day's only breakaway but they were reeled in inside the final 20 kilometres as the FDJ.fr team upped the pace in the peloton looking to set up sprint specialist Nacer Bouhanni.
The Frenchman eased past the final steep climb but came up just short in the finale, finishing fifth.
Bouhanni, who features on France's long list for the world championships, nevertheless underlined his credentials for the event later this month.
The circuit of the men's elite race in Ponferrada, Spain, features two short climbs that should eliminate the pure sprinters but Bouhanni has been showing on the Vuelta that he has what it takes to cope with that kind of challenge.
On Friday, however, Navarro anticipated the final fight and attacked the leading pack with the top guns letting him ride away.
Britain's Chris Froome, who is fourth overall, attempted a counter-attack but Spain's Alejandro Valverde and Contador chased him down.
Contador leads Valverde (Movistar) by 20 seconds and Colombian Rigoberto Uran (OPQS) by 1:08 with Froome of Team Sky lying 1:20 off the pace.
Saturday's 14th stage is a 200.8-km hilly trek between Santander and La Camperona.
(Writing by Julien Pretot; Editing by Rex Gowar)
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