Spain's Alberto Contador retained the overall leader's red jersey that he snatched in Tuesday's individual time trial.
Tinkoff-Saxo rider Contador leads compatriot Alejandro Valverde by 20 seconds and Colombian Rigoberto Uran by 1:08.
Degenkolb, who holds the green jersey for the overall points classification, was among a dozen riders who avoided the late accident as he beat Belgian Tom Boonen and Italian Jacopo Guarnieri who were second and third respectively.
"I did not see the crash, it happened behind me and I did not want to look back as I would have risked crashing myself," Giant-Shimano rider Degenkolb told reporters.
"It was not easy to find a good position in the finale because everybody was jockeying for a good spot but we managed that well."
Top sprinters Nacer Bouhanni of France and Australian Michael Matthews could not contest the sprint at the end of the 166.4-km stage as they were held up by the crash.
"I knew it would be tense," said FDJ.fr rider Bouhanni who won the points classification at the Giro d'Italia. "I had good legs, it's frustrating."
Friday's hilly 13th stage will take the peloton from Belorado to Obregon.
"It's going to be a busy day," said Contador.
(Writing by Julien Pretot, editing by Tony Jimenez)
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