Battaglin beat fellow Italians Fabio Felline and Giovanni Visconti for his first stage victory in one of cycling's main tours.
Overall favorite Bradley Wiggins lost 17 seconds after he was caught behind a crash near the finish on the slippery road. He dropped to sixth in the general standings, 34 seconds behind Paolini. Main rival Vincenzo Nibali moved up to fourth, 31 seconds off the pace.
Battaglin, who rides for Bardiani Valvole-CSF Inox, completed the hilly 153-mile route from Policastro Bussentino to Serra San Brunowon in 6 hours, 14 minutes, 19 seconds.
The Italian stayed in the main pack throughout the race while a number of other riders tried unsuccessful breakaways.
The first featured seven riders who built a lead of nearly eight minutes after 34 miles. But the pack, 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 six miles to go, bringing Robinson Chalapud with him.
Georges ran out of steam and dropped back to the main pack while Di Luca and Chalapud stayed 10 seconds in front heading over the summit. They were caught with less than a half mile remaining to set up the mass sprint to the line.
Wednesday's fifth stage is a mainly flat, 124-mile leg from Cosenza to Matera.