It was the biggest victory of his career and capped a great day for the Bora-Hansgrohe outfit as Italian Cesare Benedetti claimed the early lead in the king of the mountain category after spending all day in a breakaway.
Australia's Caleb Ewan (Orica-Scott) was second over the line with Germany's Andre Greipel (Lotto-Soudal) third.
All the main GC contenders, including Movistar's Columbian favourite Nairo Quintana and Team Sky's co-leader Geraint Thomas, finished safely in the pack after a late crash which held up the peloton.
The day begun in sombre fashion with a minute's silence at the start in memory of Italian former Giro winner Michele Scarponi was who killed last month.
His former Astana team mates then led the riders away from the start in Alghero before an early breakaway formed with Benedetti joined by five others including Eritrean national champion Daniel Teklehaimanot (Dimension Data).
Benedetti won each of the day's three fourth category climbs and was still part of a four-man bunch that was swallowed up on a fast descent into Olbia inside the final three kilometres.
From there it seemed set for the powerhouses like Greipel but two-year professional Postlberger went out and opened up a gap that proved decisive.
"We wanted to try for a sprint for the final for (team mate) Sam (Bennett). Through the city the lead-out trains, I don't know, they lost my wheel or something and I had a gap," Postlberger, who even had time to raise his arms in celebration before the finish, said.
"I heard over the radio, 'C'mon, Posty go try!' and I put all I have in. It worked out, victory for the team, first professional victory for me -- maglia rosa. I think I will need many weeks to realise this victory. It's unbelievable."
Saturday's 221km second stage takes the riders through the centre of the island from Olbia to Tortoli and after some medium-range climbs should result in a bunch sprint.
(Reporting by Martyn Herman, editing by Pritha Sarkar)
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