Team Sky completed the highly technical 17.4km course in a time of 22 minutes and five seconds to beat Movistar by nine seconds and the Astana team of Wiggins's big rival, Vincenzo Nibali, by 14 seconds.
Twenty-three-year-old Italian Puccio, riding his debut Giro d'Italia, was one of five riders from Team Sky who crossed the line to set the best time. Puccio tops the general classification by virtue of his placing in Saturday's opening stage. He is tied at the top with Wiggins, fellow Italian Dario Cataldo and Colombian pair Rigoberto Uran and Sergio Henao.
Overnight leader Mark Cavendish, the former Team Sky sprinter, lost the maglia rosa after his Omega Pharma-Quick Step team could only post the 17th best time, 48 seconds slower than Sky. Cavendish swapped the pink jersey for the red points jersey on the back of his victory in Saturday's opening stage in Naples.
It was the first time the Corsa Rosa had visited the picturesque island of Ischia in 54 years. Under a bright sun and temperatures in the high 20s, each of the race's 23 teams tackled a demanding course that featured four climbs and numerous bends.
Spanish outfit Movistar produced the surprise of the day, bettering Sky by two seconds at the first check point before crossing the line nine seconds behind the British team. Movistar now have a cluster of riders nine seconds down on the Sky quintet on GC, with Spaniard Benat Intxausti top of the pack in sixth place. Movistar's Giovanni Visconti retained the blue jersey as the race's best climber.
Italian race favourite Nibali - who will look to make up lost time on Wiggins in the mountains - limited his losses to just 14 seconds after a strong ride from his Astana team.
Deprived of last year's Giro runner-up Joaquim Rodriguez, Katusha nevertheless set the fourth best time at 19 seconds while Italian wildcards Vini Fantini took fifth. The Pro Continental team crossed the line 22 seconds down on Sky and level with fellow Italian outfit Lampre.
Victors in last year's team time trial in Verona, the Garmin-Sharp team of defending champion Ryder Hesjedal were uncharacteristically disorganised in their race against the clock, coming home 25 seconds off the pace.
Blanco Procycling - the former Rabobank team of Dutch 'eternal hope' Robert Gesink - set the early benchmark time but slipped to eighth at the finish, 28 seconds in arrears and tied for time with Orica-GreenEdge.
The BMC team of Australia's Cadel Evans took 12th at 37 seconds while Dutch team Argos-Shimano brought up the rear, 1:13 down on winners Sky.
With Bradley Wiggins in a commanding position as he bids to become the first Briton to win Italy's major stage race, the Giro continues on Monday with the undulating 222km stage three from Sorrento to Marina di Ascea on the Mediterranean coast.