Battaglin, who rides for Bardiani Valvole-CSF Inox, won in a time of 6 hours, 14 minutes, 19 seconds along the hilly 246-kilometre route from Policastro Bussentino to Serra San Bruno.
The 23-year-old rider 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 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. Defending champion Ryder Hesjedal of Victoria moved into fifth overall after finishing eighth in Tuesday's stage.
Wednesday's fifth stage is a mainly flat, 199-kilometre leg from Cosenza to Matera.
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