The Slovenian blitzed the 8km test, which finished on top of a steep 2.1km climb to the Sanctuary of San Luca, in 12:54 to become the first wearer of the pink jersey.
“I’m super happy,” the 29-year-old Jumbo-Visma leader said shortly after the conclusion of the stage. “It is a really nice feeling to get a victory.”
He explained that he did not have a specific tactic for the stage other than going “through the whole course as fast as possible”.
“And, yes, I think we did a good job.”
Roglic, whose victory in last week’s Tour de Romandie included a triumph in the final-day time-trial, said he was surprised at the size of the gap to his rivals.
“You always want more and more but a win is a win. The first day is behind us and it is a really nice start.
“But the most important thing is to wear it (the maglia rosa) in Verona at the end. It is a great start and I’m looking forward to the next three weeks.”
With bad weather in the air, Roglic was one of several pre-race favourites who rolled the dice with an early start and it paid handsome dividends.
Tom Dumoulin (Sunweb), the first rider to leave the start house, clocked 13:22. However, the 2017 champion’s stay at the top of the leaderboard was short-lived after Miguel Angel Lopez (Astana) bested him by a fraction of a second.
They were soon eclipsed by two-time former champion Nibali, who lowered the benchmark by a further five seconds.
But the Italian, who at 34 is aiming to become the oldest winner of the Corsa Rosa, was no match for a storming Roglic, who crossed the line 23 seconds faster.
The early pacesetters had to wait several hours for Yates to finish after the Briton, many pundits’ favourite for overall honours, opted for a later start and was the second last rider to set off.
His challenge seemed to be fading when he reached the 5.9km checkpoint 18 seconds down on Roglic, but the 2018 Vuelta a Espana winner made the most of the final climb to secure the runner-up position.
The 102nd Giro d’Italia continues tomorrow with a 205km stage from Bologna to Fucecchio before concluding in Verona on June 2.