Martin showed attacking intent and tried to break away from the chasing group with 10km to go, but was quickly reigned in on the descent of the Col de la Colombiere.
Keen to limit the time gap, the Stage 6 winner pushed up the final kick to secure a respectable seventh place and remain in the hunt overall in 17th place – five minutes off the pace.
Frenchman Julian Alaphilippe (Quick-Step Floors) won the stage after breaking away early and looking in full control as he crossed the line 01:34” in front of his nearest rival.
Greg Van Avermaet extended his lead in yellow to more than two minutes with a superb ride.
The BMC rider crossed the line fourth on the stage but one minute 39 seconds ahead of the main group of contenders, which included Team Sky’s Chris Froome and Geraint Thomas, plus Adam Yates of Mitchelton-Scott.
That saw the Belgian extend his overall lead to two minutes and 22 seconds over Thomas, with Movistar’s Alejandro Valverde up to third.
Irishman Martin said: “It’s nice to get the first one out of the way. It’s always a bit nervous after the rest day. I’m pretty happy with that. It was a block head wind (on the final climb), every bone in my body said don’t attack.
“But I knew if guys were five or 10 seconds off the back, by the time we reach the bottom it could be one minute. The next two days are going to be brutal and I’ll see how my legs are – but I expect a lot more attacks tomorrow.”
There will be little time for riders to recover as they look ahead to another tough day in the mountains and battle a 108.5km route from Albertville to La Rosiere.
These parcours have already featured on this year’s UCI World Tour – as part of Stage 6 of the Criterium du Dauphine – so will be familiar to many of the riders.
Martin picked up a top five finish on that stage in June so will be hopeful of a strong performance as he hunts a second Tour de France stage victory.
Greg Van Avermaet extended his lead in yellow to more than two minutes with a superb ride as Julian Alaphilippe won Stage 10 of the Tour de France.
Van Avermaet was expected to surrender the race lead he has held since the Stage 3 team time-trial as the race moved into the Alps on Tuesday, but the Olympic champion defied predictions as he joined a breakaway and stayed away on the road to Le Grand-Bornand.
The BMC rider crossed the line at the end of the 158.5-kilometres route from Annecy fourth on the stage but one minute 39 seconds ahead of the main group of contenders, which included Team Sky’s Chris Froome and Geraint Thomas, plus Adam Yates of Mitchelton-Scott.
That saw the Belgian extend his overall lead to two minutes and 22 seconds over Thomas, with Movistar’s Alejandro Valverde up to third, three minutes and 10 seconds back.
Alaphilippe, 26, delivered his first career Tour stage win after moving off the front of the break at the summit of the Col de Romme, 28.5km from home.
The Quick-Step Floors rider gradually pulled away as he turned a bid for the climbers’ polka-dot jersey into a first French stage win of this Tour.
After his BMC team-mate Richie Porte crashed out of the Tour on Sunday, Van Avermaet started the second week with no agenda but to stay in yellow as long as he could, and put in a ride to honour the jersey here.
He joined an 18-strong break that had moved seven minutes clear by the time they crested the summit of the Montee du plateau des Glieres, heading on to the gravel roads over the plateau made famous by the French resistance in World War II.
Sky were pacing the peloton behind but, after slowing the pace to wait for Froome – who suffered a puncture on the gravel – they could not fully reel in the break.
UAE Team Emirates’ Dan Martin is hoping the injuries sustained in a stage-eight crash will not slow him down now the Tour de France has reached his favoured terrain in the mountains.
The Irishman celebrated victory on the Mur-de-Bretagne on stage six but was among the general classification hopefuls caught out in the chaotic opening week of the Tour.
He crashed heavily on Saturday’s stage eight to Amiens and suffering cuts and bruises on his back, hip and elbow.
“The power is still there and the condition is still good,” the 31-year-old said on Monday’s rest day.
“It’s far from ideal, if you crash on the Tour de France its going to impact your recovery on a long-term scale but though yesterday was difficult the rest day has given my body a chance.”
The last thing Martin needed the day after a heavy tumble was a stage over the rough cobbles of northern France, but that is precisely what Sunday’s stage nine to Roubaix delivered.
Martin dodged the carnage which ended Richie Porte’s race and caught out Chris Froome, Rigoberto Uran and Romain Bardet among others, and managed to come out smiling.
“The main thing for me was to not crash,” he said. “There was a bit of a fear factor, when you’ve had a really scary crash and you go back into that battle zone, it’s hard psychologically.
“But what an experience it was. It was kind of cool to race the cobbles. That’s how I’m approaching this whole Tour de France, just to enjoy it for what it is. It’s a crazy moving circus around France and every day is different.”
Though he finished with a smile, posting pictures alongside his team-mates of their dusty faces, Martin revealed there was at least one x-rated picture that was held back as some of his stage eight wounds reopened.
“There was blood seeping through my jersey,” he said. “I had one pretty disgusting photo of my jersey at the finish line but the guys said, ‘You can’t really post that’ and I guess they were right.
“But it’s kind of remarkable how I’ve bounced again. I’ve got a big bruise on my back and on my hip but from the waist down there’s barely a scratch and that’s the bit that makes the bike go forward.”
Aside from the bruises the bigger concern for Martin on stage eight was a loss of 76 seconds which saw him slip to 24th overall, three minutes 22 seconds off yellow and almost two minutes down on the likes of Froome and several other overall contenders.
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 last year.
Though he has yet more bumps and bruises, he is not changing his approach to the race.
“That’s what I keep thinking to myself,” he said. “It isn’t easy, but it’s easier than last year.”