Race favourite Wiggins of Team Sky crossed the line in a second group 17 seconds behind the winner, Battaglin of Italian wildcard team Bardiani Valvole, to drop from second to sixth on GC.
The 2012 Tour de France champion was held up after three riders hit the deck in Apocalyptic conditions towards the finish. Although the incident happened in the closing 3km, the race jury only awarded the three riders who crashed the same time as the stage winner.
Following the controversial decision, Wiggins is now level on time with defending champion Ryder Hesjedal of Garmin-Sharp and 34 seconds behind the pink jersey Luca Paolini (Katusha).
Twenty-three-year-old Battaglin produced the ride of his career to reel in escapee Danilo Di Luca (Vini Fantini) inside the closing 100 metres before taking the victory in Serra San Bruno by a couple of bike lengths ahead of fellow Italians Fabio Felline (Androni Giocattoli) and Giovanni Visconti (Movistar).
“I was good yesterday and I hoped to win," Battaglin said, "but in the end it felt more like a Moto GP than a bike race and I was dropped.
“Today the climb suited me, the rain might have stopped some riders, and the gradient wasn’t too hard, and even though I attacked a bit early, it went well.”
He continued: “In 2011, after I had won everything as an amateur, I started my pro career winning at the end of 2011 [he won the Coppa Sabatini in October 2011].
“Perhaps I thought it was easier than it really is. I may have paid for that last year [when he failed to win once in 2012].
“This year, I was determined to show that I’m a good rider. I worked hard in the winter and I’m starting to reap the rewards.”
Team Sky's Rigoberto Uran crossed the line in fourth place - but in heavy mist and lashing rain there was no sign of the Colombian's team leader Wiggins, who lost touch with the main group during the 6km run into the finish following the second of two categorised climbs towards the end of the long 246km stage.
Uran is now second on GC, 17 seconds behind Paolini, with Spaniard Benat Intxausti (Movistar) third at 26 seconds.
Italian favourite Vincenzo Nibali suffered a scare on the descent of the penultimate climb of the day, 35km from the finish, when picking up an untimely puncture.
But 2010 Vuelta champion Nibali was able to swap wheels with Astana team-mate Valerio Agnoli and finished safely in the main group. He rises to fourth on GC, 31 seconds down on the maglia rosa Paolini.
A break of seven riders - Julien Berard (Ag2R-La Mondiale), Emanuele Sella (Androni Giocattoli), Miguel Minguez and Ioannis Tamouridis (both Euskaltel), Johan Le Bon and Francis Mourey (both FDJ) and Pim Ligthart (Vacansoleil-DCM) - rode off the front of the peloton shortly after the start of the Giro's second longest stage at Policastro Bussentino.
The seven escapees forged a maximum lead of just over seven minutes on the coastal roads heading to the toe of Italy.
But the presence of Sella - just 2:39 down in the overnight standings - meant that the Katusha team of race leader Paolini were wary of the break building up too much of an advantage.
When Sella, Tamouridis and Mourey were dropped by the leading group it looked like the game was back on for the escapees. The lead grew from three minutes to just under the five-minute mark with around 70km remaining.
This gap, however, had been whittled down to just two minutes when the race reached the first real test of the day, the Cat.3 Vibo Valentia.
Minguez attacked with Berard but both riders were reeled in before the summit as Stefano Pirazzi (Bardiani Valvole) jumped clear to take the points over the top.
By this point, the sun and blue skies from the coastal road had been replaced with rain and mist - making for a nervous conclusion to the stage.
A new five-man break formed around Pirazzi and Marco Marcato of Vacansoleil-DCM. Frenchman Sylvain Georges (Ag2R-La Mondiale) then went for broke at the start of the Cat.2 Croce Ferrata 18km from the finish.
Georges held a one-minute advantage over the main pack, which was being controlled by Team Sky and Katusha, when Di Luca made his move.
The controversial Italian veteran - who won the Giro in 2007, two years before being banned for testing positive to CERA (third generation EPO) - powered clear of the pack, taking Colombia's Robinson Chalapud in tow.
Georges was soon caught before the leaders crossed the summit with a slender advantage over the pack.
Rolling back the years, Di Luca looked like he would defy the onslaught of the peloton. The 37-year-old seemed to have given up as he passed under the kite - but was stirred by a last-ditch blast by his Colombian colleague.
Neither rider quite had the strength to withstand the pack - and Di Luca was swept up agonisingly close to the finish.
Battling through the rain, Battaglin surged ahead of the rest of the field to take the win in his second appearance in the Giro d'Italia.
Felline and Visconti were left to fight for the scraps - although the latter managed to take back the blue mountains jersey after taking third place over both summit ahead of his third place at the finish.
Australian Cadel Evans of BMC finished strongly in sixth place to ride to 10th in the overall standings, 42 seconds behind Paolini.
The Giro continues on Wednesday with the 203km stage five from Cosenza to Matera, which concludes with another succession of punchy climbs.
Stage four result:
1 Enrico Battaglin (Ita) Bardiani Valvole-CSF Inox 6:14:19
2 Fabio Felline (Ita) Androni Giocattoli -
3 Giovanni Visconti (Ita) Movistar Team -
4 Rigoberto Uran Uran (Col) Sky Procycling -
5 Arnold Jeannesson (Fra) FDJ -
6 Cadel Evans (Aus) BMC Racing Team -
7 Benat Intxausti Elorriaga (Spa) Movistar Team -
8 Ryder Hesjedal (Can) Garmin-Sharp -
9 Robert Kiserlovski (Cro) RadioShack Leopard -
10 Luca Paolini (Ita) Katusha
Top 10 in General Classification:
1 Luca Paolini (Ita) Katusha 15:18:51 -
2 Rigoberto Uran Uran (Col) Sky Procycling 0:00:17 -
3 Benat Intxausti Elorriaga (Spa) Movistar Team 0:00:26 -
4 Vincenzo Nibali (Ita) Astana Pro Team 0:00:31 -
5 Ryder Hesjedal (Can) Garmin-Sharp 0:00:34 -
6 Bradley Wiggins (GBr) Sky Procycling -
7 Giampaolo Caruso (Ita) Katusha 0:00:36 -
8 Sergio Luis Henao Montoya (Col) Sky Procycling 0:00:37 -
9 Mauro Santambrogio (Ita) Vini Fantini-Selle Italia 0:00:39 -
10 Cadel Evans (Aus) BMC Racing Team 0:00:42