The Tour de France champion lost 17 seconds as the peloton split in the final kilometres that included a quick descent followed by a flat section, which riders tackled in heavy rain with a cobbled section in the home straight.
Wiggins dropped from second to sixth overall, 34 seconds adrift of Italian Luca Paolini who retained the pink jersey after finishing safe in the bunch.
The Briton was one of several riders held up behind a crash involving Juan Manuel Garate, Cristiano Salerno and Laurent Pichon, which happened with less than two kilometres left in the stage.
International Cycling Union (UCI) regulations state that a rider who is held up in this way in the final three kilometres – with the exception of uphill finishes – is credited with the same time as the main bunch.
Herve Broecke, president of UCI commissaires on the Giro, explained, however, that the “three-kilometre” rule could not be applied to Wiggins as he had already dropped back.
“Wiggins was already behind the bunch when the crash took place because there was a split in the peloton, which was very strung out,” he said.
“The crash took place with less than three kilometres to go, we watched to see who had been affected by this crash and they were given the time of the riders they were with.”
Team Sky principal Dave Brailsford played down the impact of Wiggins’s time loss.
“It’s like anything, you’d prefer it not to happen, but I don’t think it’s race changing,” he said.
“It puts him back on a par with everyone else. I think the big gaps will appear in the time trials and the big mountain stages, that’s where this race is won and lost.
“On these early stages, you win some seconds here, and you lose seconds there.”
Sky’s directeur sportif at the event, Marcus Ljungvist, added: “It’s one of those things that happens in bike racing. It’s certainly not the end of the world.
“On the last climb we wanted to stay out of trouble and hold position there.
“The team rode well there. Everything is good within the team. The guys are strong.”
Other pre-race favourites Cadel Evans of Australia, Italian Vincenzo Nibali and defending champion Ryder Hesjedal of Canada came home safe after a 246km undulating trek from Policastro Bussentino.
Paolini leads Colombian Rigoberto Uran of Team Sky by 17 seconds with Spain’s Benat Inxausti in third 26 seconds off the pace for Movistar.
Nibali and Hesjedal leapfrogged Wiggins and are now fourth and fifth, 31 and 34 seconds off the pace respectively.
Nibali, however, survived a scare with 35 kilometres remaining when he suffered a mechanical problem but managed to get back into the bunch after team mate Valerio Agnoli gave him his wheel.
With the second-category Croce Ferrata climb looming, several riders, among them Frenchman Sylvain Georges, tried their luck, jumping away from the main pack. Team Sky moved to the front of the peloton, set a decent pace and toyed with the Frenchman.
Danilo Di Luca, the 2007 Giro winner, and Robinson Chalapud of Colombia also attacked and whizzed past Georges but the Italian was reined in in the final straight as Battaglin launched a perfectly-timed sprint.
Fabio Felline (Androni Giocattoli) and Giovanni Visconti (Movistar) finished second and third respectively.
Today’s fifth stage takes the peloton over 203 kilometres from Cosenza to Matera.