Martin arrived in France looking to test himself in the general classification after defying two broken vertebrae in his back - suffered in a stage-nine crash - to finish sixth overall past year.
Despite missing out on the stage victory, Van Avermaet had the consolation of extending his lead in the general classification to 43 seconds to second place Geraint Thomas. "We're in a good position as we head into the Alps".
I honestly believed that if Richie could get through this stage he would be a realistic chance of winning this Tour de France.
Neither of their falls were as serious as that of Porte, whose race was ended by a stage nine crash for the second successive year.
There was more misfortune for BMC as Tejay van Garderen, who should assume the team leadership in the mountains, also crashed and could not chase back on, falling from third to 30th overall.
"I think it's fantastic, I can't find the right words to express how it feels to win", said Degenkolb, who now has stage wins in all three Grand Tours.
Forecast: Heavy storms coming to Brooklyn Tuesday
Sunshine and warm temperatures once again in the forecast today with highs topping out in the upper 80's to mid 90's. Comfortable conditions are expected for Wednesday through Friday , with daytime highs expected in the low 80s.
"I've waited for this victory for so long", said Degenkolb, after his maiden stage win at the race.
Trek Segafredo's Degenkolb outsprinted Van Avermaet and Yves Lampaert to win.
Van Avermaet picked up a one-second bonus overall during an intermediate bonus sprint at 20K from the finish.
Among the favorites in the overall standings apart from Froome: Alejandro Valverde is fifth (1:31 behind); Rafal Majka sixth (1:32); Jakob Fuglsang seventh (1:33); Adam Yates ninth (1:42); Landa 10th (1:42); Vincenzo Nibali 12th (1:48); Tom Dumoulin 15th (2:03); and Bardet 17th (2:32).
The BMC team leader broke his collarbone and pelvis in last year's crash and was faced with the same decision to abandon after today's crash. "When I saw these crashes I was on the brakes more often than usual because I just didn't want to end up somewhere in a hospital in France".
"I'm feeling good and optimistic about the upcoming stages", the four-time champion said on Monday, the Tour's first rest day.
Mikel Landa and Rigoberto Uran also took tumbles, the latter losing almost a minute and a half on the general classification group.