Movistar’s Amador outsprinted fellow escapees Jan Barta (NetApp) and Alessandro De Marchi (Androni Giocattoli) to take the first professional win of his career in cold and wet Cervinia.
The trio – who held an eight-minute lead over the peloton at the start of the final 26km climb – were almost caught by Garmin-Barracuda's Hesjedal, who attacked with gusto from a group of race favourites on the final climb of the 206km stage from Cherasco and finished 20 seconds down in fourth place.
Hesjedal's late attack means he overturned a 17-second deficit on overnight race leader Joaquim Rodriguez (Katusha), who finished with a cluster of big names a further 26 seconds back.
"I felt good today," Hesjedal told Eurosport after regaining the pink jersey he lost to Rodriguez after the Spaniard's stage 10 win at Assisi.
"Liquigas were setting the tempo but they started to ease off so I decided to give it a go. My legs felt good. I decided to test myself - and to test the race. It worked out well."
With his latest accomplished performance in the mountains, the 31-year-old Canadian has underlined his credentials as a main contender for the race, which finishes with an individual time trial in Milan next Sunday.
Hesjedal now leads Rodriguez by a slender nine seconds in the GC, with Italian Paolo Tiralongo (Astana) in third at 41 seconds. Ivan Basso, whose Liquigas team yet again set the pace over the two major climbs of the day, finished the stage in the chasing group with Rodriguez to retain his fifth place, 1:06 down.
The Giro's first major rendezvous with the high mountains started with a long and fast 140km flat slog in which speeds reached as high as 50kmh. With such a devastating tempo being set it took until the 70-kilometre mark before a breakaway established itself on the road.
Instigated by Olivier Kaisen of Lotto Belisol, the eight-man break had built up lofty lead of 13 minutes before the start of the Cat.1 Col de Joux.
Moments into the 22-km-long climb, Barta upped the tempo and rode off the front. Both Amador and De Marchi formed a chasing group alongside Matteo Montaguti (Ag2R-La Mondiale) and Pierpaolo De Negri (Farnese Vini).
Barta crossed the summit a huge 11:25 ahead of the peloton and almost a minute ahead of his four pursuers. But slippery roads saw the Czech rider take the descent very gingerly.
The opposite could be said of Amador, who descended like a man possessed to open up a lead on the front of the race. The 25-year-old from Costa Rica pulled out a lead of more than a minute on his fellow escapees despite almost coming a cropper on numerous occasions.
Amador looked set to ride all the way to the summit of the final Cat.1 climb on his own, but he soon tired, allowing first De Marchi and then Barta to rejoin him on the front.
Meanwhile, the Liquigas train - led by Basso’s super domestique Sylvester Szmyd - was thinning out the chasing peloton, which was eating into the trio's lead at a mind-blowing rate of almost a minute every kilometre.
The attacks came thick and fast, with Venezuelan Jose Rujano (Androni) and Spaniard Mikel Nieve (Euskaltel) both trying their luck.
But it was Hesjedal who made the decisive move, counter-attacking Nieve’s attempt to break clear inside the final 3km to open up a gap over his rivals.
Pink jersey Rodriguez attempted to reel him in, but the Katusha climber found his acceleration foiled by defending champion Michele Scarponi (Lampre).
As the drama played out, the three leaders passed under the 1km-to-go banner with their huge lead whittled down to a matter of seconds.
Barta attacked first, but Amador proved too strong, while De Marchi had no gas left in the tank. The Movistar rider crossed the line ahead of an exhausted Barta, with De Marchi two seconds back in third.
Hesjedal had ridden the final flat kilometre with real verve to cut the deficit to just 20 seconds - and the count was on.
Tiralongo led the chasing group over the line 46 seconds down on Amador, with Team Sky's Rigoberto Uran – the new white jersey – and Rodriguez right on his wheel.
Hesjedal's bold move had paid off: the maglia rosa was back on the Canadian's shoulders.
The Giro continues on Sunday with the 172km stage 15 which includes four classified climbs including the summit finish in Piani dei Resinelli.