The German had the legs in a three-man sprint to the finish after he, Yves Lampaert and yellow jersey holder Greg Van Avermaet broke away with 16km remaining.
Despite his tour upset, Porte said he has his eye on future competitions.
Mikel Landa also lost seven seconds, having crashed while trying to take a drink from his bottle before being paced back by his Movistar squad as their other leaders, Nairo Quintana and Alejandro Valverde, finished safely in the main bunch.
Degenkolb's victory came at the end of a crash strewn stage, which lived up to expectations of being a key one for general classification contenders.
But such is the form of world road race champion Sagan, who flew over the cobbles from 50km out to win the one-day race this spring, few would bet against him adding yet another stage win to his growing haul.
Affaire Lactalis : les députés veulent plus de rigueur dans les contrôles
Il y a un moment, " il faut que ce soit très clair: un numéro unique, un site unique, une décision unique ", a-t-il déclaré. Une hypothèse qui a été rejetée par Bruno Le Maire le 14 juin, lors de son audition devant la commission d'enquête.
"This is such an awesome feeling for me because I've had so many second places at the Tour since winning my first stage in 2013", said the 31-year-old.
Australian Richie Porte pulled out after an early crash.
Romain Bardet, the French hope who finished on the podium the last two years, struggled through three punctured tires but kept his losses to a minimum.
Degenkolb was the victim of a serious training accident in January 2016 when a vehicle drove into oncoming traffic.
Arizona earns hosting duties for 2024 Final Four
Four powerhouse programs - Kentucky, UConn, Kansas and Villanova - have won national championships in San Antonio . The city hosted in 1971, when UCLA won its fifth of what would be seven consecutive national championships.
Green jersey Peter Sagan, this year's Paris-Roubaix champion after an attack from 53km, was furious with himself after a lapse cost him a place on the winning break. "When you hear a doctor say that you know it's no good", he said.
The 109-mile stage features three beyond-category climbs - Col de la Madeleine, Croix-de-Fer and the iconic Alpe d'Huez finish after 21 switchbacks to close out the Tour's three days in the Alps. "I had been through a lot of things in the past and it was such a hard time".
The route starting in Arras contained the highest number of cobblestone sections since the 1980 Tour, with almost 22 kilometers altogether.
The peloton will get a well-earned day of rest on Tuesday before heading into the mountains for stage 10 on Tuesday.
Audi TT gets fresh face, more standard equipment for 2019
Headlights with LED or Matrix LED technology are optionally available, and now include Audi's "swiping" indicators. The base TT sees 17-inch wheels standard, while the TTS gets 18s; 19- and 20-inch wheels are optional.