"It's L'Angliru, it's mythical. This morning if you'd have told me this I wouldn't believe it," Elissonde said.
Horner collapsed to the ground after pedaling across to the finish line second, 26 seconds after Elissonde. After soaking up being close to the biggest win of his long career, he was helped to his feet by race officials.
Joaquim Rodriguez's Katusha team set a brutal pace on the last two peaks, whittling down the group of favorites to 11 riders with seven kilometers to go.
The L'Angliru summit was teeming with fans, many of who had camped out overnight to be there the next day to encourage the tired cyclists on their way up.
Horner withstood Nibali's series of challenges on the ascent reaching 23 degrees of incline, with the narrow mountain road crowded on both sides by raucous supporters and with thick fog limiting visibility to a few meters (yards).
And when the Astana rider had apparently spent all his energy, Horner pulled away using his high-riding stance.
"I tried everything I could, but I couldn't do it," said Nibali. "It was impossible to shake Horner. I have to settle for second place, but I am not happy."
Horner praised Nibali and Spaniards Alejandro Valverde and Rodriguez.
"To have those guys around me for this victory is unbelievable," said Horner. "That Nibali would put such an attack at the finish like that and make it so epic and unbelievable for the fans, to see him attack 10-15 times - whatever it was - I'm sure the fans must have been on the edge of their seats every moment of it, of every pedal stroke that I did on the final climb."
Former winner Valverde will complete the podium. The Movistar rider is 1:36 behind Horner, with Rodriguez a distant fourth at 3:22 back.
"Horner was the strongest and we have to congratulate him for the victory," Valverde said. "His performances surprised us at the beginning, but not now."