Degenkolb, who rides for Argos-Shimano, won in four hours 37 minutes 48 seconds along the mainly flat, 199-kilometre leg from Cosenza to Matera.
It is a first stage victory in the Giro for the 24-year-old German, who finished several bike lengths ahead of Angel Vicioso. Paul Maertens was third.
Victoria's Ryder Hesjedal remained in the mix to defend his 2012 Giro title. Hesjedal remained fifth overall, 34 seconds off the pace, after finishing 24th in Wednesday's stage.
The end saw a crash in the lead group just over a kilometre from the finish line. One of Degenkolb's teammates, Luka Mezgec, crashed on the final turn, bringing several other riders down with him.
Marco Canola raced clear but the Italian was unable to hold off his pursuers.
All the riders delayed by the crash behind Degenkolb were awarded the same time, which meant Paolini kept his pink jersey.
Overall favourite Bradley Wiggins, who lost 17 seconds on Tuesday, remained sixth in the general standings, 34 seconds behind Paolini. Main rival Vincenzo Nibali was still fourth, 31 seconds off the pink jersey.
The stage had another early break and Tomas Gil, Stefano Pirazzi, Alan Marangoni, Ricardo Mestre, Brian Bulgac and Rafael Andriato swiftly built a lead of nearly 10 minutes.
Pirazzi was dropped after 35 but the remaining quintet maintained a healthy advantage.
The breakaway was swallowed up by the peloton on the first of the two climbs near the finish.
Mark Cavendish, who won on the opening day in Naples, fought hard up the climb to Montescaglioso to keep his chances of another stage victory alive.
However, he received no help on the descent and was unable to stay in contention.
Although heavy rain had stopped by the time cyclists arrived at the finish, the roads remained slippery and that perhaps contributed to the crash.
Degenkolb avoided the crash and raced in pursuit of Canola, catching him in the final 300 metres to win by several bike lengths.
Thursday's sixth stage is another mainly flat one, along 168 kilometres from Mola di Bari to Margherita di Savoia.