Kittel looked to be struggling as the leaders roared towards the finish in Troyes but the powerful German sprinter ended up winning the sprint comfortably for his 11th Tour stage victory.
"It's an unbelievable feeling to be back in yellow, but having said that I know race far, far from over, it's only just begun for me", said Froome. "There was just a moment when I broke free and started to go ahead". "I'm really happy I could throw my bike far enough to have these six millimetres".
The GC (general classification) contenders will return to proper action on Sunday for a stage featuring three out-of-category climbs and a risky descent into Chambery.
First Froome 1.7km out and then Richie Porte in the final kilometre counter-attacked behind but it was Ireland's Martin who took second place to move up to fourth overall at 25sec. It can be really close.
With Peter Sagan disqualified from this year's Tour, the race for the green jersey is wide open.
Arnaud Demare of FDJ holds it for now, but Kittel is closing in after his second win of the Tour. This was one of the tightest stage victories the Tour has ever seen, eclipsing even last year's whisker-thin margin between Kittel and Bryan Coquard at Limoges.
Aru, though, is now just 14sec back and Froome said he and his Sky team-mates would not be able to take their eyes of the Sardinian again. "It was very important for the victory", said Kittel.
"He's obviously going well but I think he's going to have more pressure on him now".
"Everyone knows that I have a lot of respect for Andre, he's also a great sprinter and a very fair and nice rider".
First comes a rolling stage eight from Dole to Station des Rousses, which will have caught the attention of breakaway specialists such as Dimension Data's Steve Cummings. It should be a big weekend of racing. "This is what we spend all season training for, to be good in the mountains".
"Tomorrow already we're going up quite a big climb with 20-25 kilometres to go, it could shake things up a bit but the bigger obstacle to come is on Sunday as we go into the Jura mountains and tackle Mont du Chat before the finish".style="text-align: center;"