The Giant-Alpecin rider stayed safe in the peloton during the 293-km ride, the longest of the World Tour season, and then easily outsprinted defending champion Alexander Kristoff of Norway (Katusha) on the Via Roma.
"Last year it was the biggest disappointment of my career," said Degenkolb, who had been ruled out of the finale with a puncture.
"And this year I add my name to the list of prestigious winners, it's the biggest win of my career."
Australian Michael Matthews took third place for Orica-GreenEdge while classic specialists Peter Sagan of Slovakia (Tinkoff-Saxo) and Swiss Fabian Cancellara (Trek) were never in the mix for the win, finshing fourth and seventh respectively.
Czech Zdenek Stybar (Etixx-Quick Step) and Belgian Greg van Avermaet (BMC), two of the in-form riders this early season, were the first big guns to attack in the Cipressa climb as some pure sprinters showed signs of weakness.
At the end of the descent of the Cipressa, Italian Daniel Oss (BMC) and Geraint Thomas (Team Sky) jumped away from the peloton but were reined in by the top of the climb to the Poggio.
World champion Michal Kwiatkowski of Poland and his team mate Stybar crashed during the descent, as well as Belgian Philippe Gilbert (BMC).
Sagan went to the front at the end of the Poggio descent but there was no way out of the pack for him or Cancellara.
Kristoff then launched his effort in the final straight too early and was overtaken by Degenkolb.
Italian Niccolo Bonifazio (Lampre) and Frenchman Nacer Bouhanni (Cofidis) took promising fifth and sixth places respectively on their Milan-San Remo debut.
The next "Monument" classic is the Tour of Flanders on April 5. It will be followed by Paris-Roubaix (April 12), Liege-Bastogne-Liege (April 26) and the Tour of Lombardy (Oct. 3).
(Writing by Julien Pretot; Editing by Ian Chadband/Alan Baldwin)
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