Last year's Tour de France winner had a mechanical problem on a climb which stymied his attempts to win the race ahead of the Italian.
Wiggins threw his Pinarello against a wall after breaking down with gear trouble, though the bike remarkably rested neatly against the rock face.
He charged up the mountain but Nibali pulled away just as Wiggins reeled in the leaders and came home in first to claim a Tirreno-Trentino double.
Italy's Mauro Santambrogio was second in the GC with Wiggins 1.40 down in fifth.
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