Narvaez (UAE Team Emirates XRG) and Mas (Movistar) were left to battle for the win after leaving the breakaway group on the final climb, and Mas made the first move, only for the Ecuadorean to overtake him before the line.
Italian Diego Ulissi (XDS Astana) won the race for third place at the end of the 195-km ride from Porcari to Chiavari.
"Mas was the strongest in the climb and I knew I had to play my game, I just tried to defend myself on the uphill," Narvaez said.
"I was scared because when he did the sprint, he almost closed me on the barriers and I was on the limit, but it was full gas racing all day, because we don't race just in the uphills, we race on the downhills also."
Italian Diego Ulissi (XDS Astana) won the race for third place at the end of the 195-km ride from Porcari to Chiavari.
No change in GC
There was no change at the top of the general classification, with Portugal's Eulalio maintaining his 27-second lead over race favourite Jonas Vingegaard.
The first half of the stage gave plenty of opportunities for breakaways from the peloton before the riders reached the first of three categorised climbs.
Early attacks were reeled in, and the group that managed to get away grew in size as others left the bunch to go in chase, before the race settled down on the second climb with a 12-man group over three minutes ahead of the peloton.
A crash on the descent brought down three of the leaders, and the breakaway began to split.
On the uncategorised climb before the finish, Mas attacked, Narvaez followed, and with the Spaniard unable to shake off the Ecuadorean before the descent, Narvaez was always going to be the favourite in a sprint finish.
Mas, a three-time runner-up in the Vuelta a Espana, is out of contention for the overall win, and the Spaniard was desperate for a stage victory on his Giro debut, but Narvaez claimed the fifth Giro stage win of his career.
The peloton, containing all the GC contenders, trailed in over three minutes behind the winner, and Eulalio (Bahrain Victorious) will wear the pink in Thursday's stage 12, a flat 175-km ride from Imperia to Novi Ligure.