The Kazakh left behind Neilson Powless (EF Pro Cycling) on the Col de la Lusette, quickly building a 30 second lead over a rallying Jesús Herrada as he crested that climb.
Lutsenko finally came home 55 seconds ahead of the brave Spaniard who lost touch with the remnants of the break several times on Lusette.
"This victory is very important for me," Lutsenko said. "This is the Tour de France, the most important race in the world. I’m very happy. I’ve worked so hard to get this victory. All this work has paid off.
"Today we talked before the start, at the bus, with our DSs and our manager Alexandre Vinokourov.
"Since I had lost quite some time in previous stages, I had the chance to go in the breakaway. I did my best on the last climb to win.
"I never actually get dropped - I just kept a steady pace. The team car was telling us on the radio there were two very hard kilometres at the second part of the climb, so I rode my tempo and gave it all at those to create a gap big enough to win."
Earlier on the stage, a flurry of activity met the drop of the flag until eight riders tried their luck after the fifth kilometre.
Nicolas Roche (Sunweb), birthday boy Neilson Powless (EF Pro Cycling), Edvald Boasson Hagen (NTT Pro Cycling), Daniel Oss, Rémi Cavagna (Deceuninck-Quick Step), Greg Van Avermaet (CCC), Jesus Herrada (Cofidis) and Lutsenko battled for a further 15 kilometres to properly snap the elastic when the peloton finally fanned across the road in approval of their escape.
After 60kms, their lead built to a maximum of around six minutes where it hovered for much of the stage as Mitchelton-Scott worked on the front for their man in yellow Adam Yates.
The break ate up the significant intermediate sprint points but Sam Bennett slightly extended his lead in green, taking six points to Peter Sagan's three.
Roche took the maximum points over the Cap de Coste KOM, the break's lead soon cut in half once the main contenders' teams woke up as the race hit the final 30kms uphill.
On the Col des Mourèzes, Roche took two more points, but Benoît Cosnefroy stays in the dots, 11 points clear of Michael Gogl.
On the Col de la Lusette, the break lost Oss and Boasson Hagen, Powless waking up the remaining escapees with an attack 22kms from the finish. Roche instantly responded as Herrada and Cavagna were dropped but Lutsenko and van Avermaet bridged.
Herrada came back a kilometre or so later and soon faded once again. Roche and van Avermaet soon lost touch and Powless attacked once again. As Lutsenko shelled Powless 18kms from the finish, Herrada rallied to stay 18 seconds within touch of Lutsenko before he stormed home.
The Tour de France continues with the 168km seventh stage from Millau to Lavaur which should be one for the sprinters but might entice the opportunists.
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