Degenkolb, who rides for Argos-Shimano, won in 4 1-2 hours along the mainly flat 124-mile leg from Cosenza to Matera.
It is a first stage victory in the Giro for the German, who finished several bike lengths ahead of Angel Vicioso. Paul Maertens was third.
The end saw a crash in the lead group just over a kilometer 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.
''My lead-out man crashed and there was just one guy in front,'' Degenkolb said. ''I looked back and saw just (Elia) Viviani behind and so I went full gas to catch the rider from Bardiani. At the end I couldn't see anything, I was so empty.
''It was a great job by my team, we controlled the whole race. We had confidence and ability and it's a great day for Argos-Shimano. It was really hard in the end. I had to suffer a lot to get to the finish.''
All the riders delayed by the crash behind Degenkolb were awarded the same time, which meant Paolini kept his pink jersey.
Overall favorite 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 22 miles but the remaining quintet maintained a healthy advantage.
Not until at the first of two climbs near the finish was the breakaway swallowed up by the peloton.
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 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 meters.
Thursday's sixth stage is another mainly flat one, along 168 kilometers (104 miles) from Mola di Bari to Margherita di Savoia.