The Team Argos-Shimano rider emerged from the carnage to pip Alexander Kristoff of Katusha to the line.
While much of the rest of the field were left to fume over a bizarre ending which saw the Orica GreenEdge bus become lodged under the race finish and a major crash rip through the peloton in the final kilometres, Kittel was celebrating a career milestone.
The 25-year-old had his debut Tour ended by illness on stage five last year but banished those demons in Bastia on Saturday.
"This is the greatest day of my life," he said. "This is absolutely something that's outstanding.
"It feels like I have gold on my shoulders.
"It's unbelievable. I have no real words for it. I'm so proud that we made it today [Saturday] and we could achieve our goal that we have actually worked years for, worked really hard for.
"I want to thank my team-mates for their really hard work. This is their success as well. They deserve it."
Mark Cavendish, Peter Sagan, and Andre Greipel, all expected to challenge for Saturday's stage honours, were caught up in the crash, with Sagan falling, Greipel appearing to suffer a puncture, and Cavendish stuck in the queue.
But Kittel had been considered a contender alongside those riders and said he did not feel Saturday's achievement had been lessened by the circumstances.
"The finish was hectic. Chaotic," he said. "There were quite a lot of crashes and then, in the end, we had to do a lead-out that was far from normal. We had to go really early, with one-and-a-half kilometres to go to the finish.
"Unfortunately some of my sprint rivals crashed today and it's always nice to compete against the best and to show that you can also win against them, not only if there's a crash.
"I'm looking forward to the next stages to sprint against Andre [Greipel] and Mark [Cavendish]. To be honest though, I don't want to even think about the next few stages; right now I just want to enjoy the yellow jersey and we'll see what happens tomorrow [Sunday]."
His pace was obvious to see as he came charging back at Kristoff in the final metres of the stage, with Danny Van Poppen in third and David Millar fourth.
"When I see the images on the television, I'm still speechless," he added.
"I was shocked, to be honest... but in the best way for how you can feel shocked! It's a dream that's come true now and I'm so, so proud for my team, myself and everyone who has supported me and believed I could win the stage today [Saturday]."