He's sitting level with Dane Jakob Fuglsang, 57 seconds behind race leader and Porte's BMC Racing teammate Greg Van Avermaet, who retains the yellow jersey.
The Irishman, victor of stage six on the Mur-de-Bretagne, was one of several riders to fall with Quick-Step Floors' Julian Alaphilippe and Tom Skujins in the polka-dot jersey also caught out.
Porte came into the Tour in winning form, taking the Tour de Suisse to stamp his claims for at least a podium finish in Paris.
Frenchman Warren Barguil, a former team mate of Degenkolb's who was also in the 2016 accident in Spain, said: "Everybody was saying he was finished, I'm so happy for him".
Most of the general classification contenders crossed the line in the main bunch but it was a costly and bruising day for UAE Team Emirates' Dan Martin, who was caught in a crash with 17km to go.
Team Sky's Geraint Thomas remains second, with Van Avermaet's team-mate Tejay Van Garderen third.
"It was some steep climbs and we were really expecting it to pick up somewhere but it never really materialised", Thomas said.
As the tour headed to the mountains for the first time following yesterday's rest day, a group of 21 riders including Van Avermaet broke early from the peleton.
"It is very emotional, I went through such a hard period so today is pure happiness", said Degenkolb, who suffered several fractures and a serious finger injury after he and some team mates were hit by a auto during a training ride in January 2016.
Up next on Stage 11 is a 108.5-kilometre (67-mile) leg from Albertville to the top of the La Rosiere summit on Wednesday.
Alejandro Valverde of Movistar moved into third overall at 3:10 off the pace.
An emotional Alaphilippe took the first Tour stage win of his career ahead of Spain's Jon Izaguirre Insausti. That will be followed by Stage 12's ascent of the legendary Alpe d'Huez.
"Dave will certainly get in both their ears and make them both think they can win it as a way of motivating them and as a way of playing this card as long as possible until there is a natural selection, a mountain stage or the Time Trail, or until there has to be a decision". The single-day race included most of the men's route.