Green jersey holder Degenkolb was among a dozen riders who avoided a late crash to beat Belgian Tom Boonen and Italian Jacopo Guarnieri, who were second and third respectively.
Top sprinters Nacer Bouhanni of France and Australian Michael Matthews could not contest the final sprint at the end of the 166.4-km stage as they were held up behind a crash in the finale.
Spain's Alberto Contador retained the overall leader's red jersey that he snatched in Tuesday's individual time trial.
The Tinkoff-Saxo rider leads compatriot Alejandro Valverde and Colombian Rigoberto Uran.
Friday's hilly 13th stage will take the peloton from Belorado to Obregon.
(Writing by Julien Pretot; Editing by Toby Davis)
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