Battaglin beat fellow Italians Fabio Felline and Giovanni Visconti in a bunch sprint on rainy, cobbled streets to claim his first Grand Tour stage victory.
Overall favourite Bradley Wiggins provisionally lost 17 seconds after being caught behind a crash near the finish in the slippery conditions and slipped to sixth in the general standings, 34 seconds behind Paolini.
Main rival Vincenzo Nibali moved up to fourth, 31 seconds off the pink jersey.
"It was so nice to go to the start wearing the pink jersey," Paolini said. "This jersey shows that the team was great today, too. Bit by bit, I'm beginning to think I can do something in the standings. Who knows?"
Defending champion Ryder Hesjedal of Victoria moved into fifth overall after finishing eighth in Tuesday's stage.
The 23-year-old Battaglin, who rides for Bardiani Valvole-CSF Inox, won in a time of six hours 14 minutes 19 seconds along the hilly 246-kilometre route from Policastro Bussentino to Serra San Bruno.
"I was good today, even if the rain at the end affected me a bit," Battaglin said. "I managed to take a couple of curves well, have a good finish and win. The cobbles certainly didn't help as my bike kept jumping, but I saw there weren't any wheels behind me and I realized I could do it."
The Italian stayed in the main peloton throughout the race while a number of other riders tried a series of unsuccessful breakaways.
The first featured seven riders who built a lead of nearly eight minutes after 55 kilometres but the peleton — led by Paolini's Katusha team — gradually reeled them in.
Several other riders tried to attack but were unsuccessful, with Sylvain Georges having the best attempt as he stormed up the final climb to Croce Ferrata. But Danilo Di Luca chased him down with less than 10 kilometres to go, bringing Robinson Chalapud with him.
Georges ran out of steam and dropped back to the peleton while Di Luca and Chalapud stayed 10 seconds in front heading over the summit but were caught with 700 metres remaining to set up the mass sprint to the line.
Wednesday's fifth stage is a mainly flat, 199-kilometre leg from Cosenza to Matera.