The nine-man team, which includes Sir Bradley Wiggins, finished the 17.4 kilometre course nine seconds ahead of second-placed Movistar, with Astana a further five seconds back.
The result means Sky Procycling’s Salvatore Puccio will wear the leader’s pink jersey today based on Saturday’s classifications, with Wiggins second and team-mate Sergio Henao completing the overall top three with the same time.
Mark Cavendish will wear the red jersey for overall points leader in the 222km route to Marina Di Ascea after his Omega Pharma Quick-Step team finished in 17th place.
Team Sky took the plaudits on the second day after they crossed the line with five riders in a time of 22 minutes and five seconds.
For Puccio, a 23-year-old Italian debutant, being presented with the race leader’s maglia rosa jersey was a proud moment.
“Today was an incredible result and it is a huge surprise. I could never have thought this morning that I would be pulling on the maglia rosa. It is incredible,” Puccio told teamsky.com.
“Once again the team showed how strong we are. Everyone put in a huge effort and it is very satisfying to be part of a big team result like this.
“For an Italian rider the maglia rosa is one of the best things that can happen to you.”
Puccio took the jersey from Cavendish, after his team were unable to maintain the 20-second buffer he earned with Saturday’s opening stage win.
Yesterday’s stage was the first time the Giro has visited the island of Ischia, and Blanco Cycling had set the early pace with a time of 22 mins 33 secs, but they were soon blown away by Team Sky’s impressive time.
Katusha, Lampre-Merida and Movistar all mounted serious challenges as they posted competitive intermediate split times, but they were unable to maintain their consistency.
Euskaltel struggled yesterday and they lost more than a minute on the overall lead in what were farcical circumstances.
Each team’s score is recorded as the time of their fifth man, and with less than a kilometre to go, Euskaltel had dropped all but four of their riders.
Knowing that their time would not matter, the four men coasted to the line, looking behind them for their team-mate, as they finished in 22nd place, one minute and one second behind Team Sky.
As the race moves on to Marina di Ascea today, Puccio has a good chance of holding on to the leader’s jersey with the sprinters’ teams looking for a bunch finish.