The German, who leads the points classification, timed a late surge to perfection at the end of Wednesday's 17th stage, a long and bumpy 190.7 kilometre ride through Galicia, which began in the port of Ortigueira.
Giant-Shimano rider Degenkolb pipped Australia's Michael Matthews (Orica GreenEDGE) and Swiss Fabian Cancellara to the line in a bunch sprint after the two surviving riders from the breakaway, Rohan Dennis (BMC) and Elia Favilli (Lampre-Merida) were caught in the final kilometre.
Overall leader Alberto Contador (Tinkoff-Saxo) finished in the peloton, maintaining his one-minute-36-second advantage over Spanish compatriot Alejandro Valverde (Movistar), who is three seconds ahead of Team Sky's Chris Froome.
Two riders were unable to line up at the start, with one of Froome's support riders Christian Knees withdrawing from the race through illness, while Rigoberto Uran of Omega Pharma-Quick-Step pulled out with asthmatic bronchitis.
The stage represented perhaps the last chance for the sprinters to prove their quality in this year's Vuelta, and it was Degenkolb that once again came out on top to move 35 points clear in the points classification.
A quintet including Dennis and Favilli broke clear 20km into the stage, however, Caja Rural's Lluis Mas Bonet, Daniel Teklehaimnot of MTN-Qhubeka and Bob Jungels of Trek Factory Racing all eventually fell away from that group.
Dennis and Favilli were unable to maintain their advantage in the closing kilometres of the stage, which were marked by a series undulations and a small cobbled hill.
Australian Dennis attacked with 1.5km to go, but that move proved in vain as the leaders were swept up by the chasing pack, with Degenkolb serving up another demonstration of his power to take triumph.