Lutsenko launched a solo attack on a day punctuated by falls on the treacherous descending sections, but had his lead cut when he misjudged a corner.
And the Kazakh rider went down again going into the run-in, denying his chances of staying away for the duration.
Having been caught by the chasing trio of Adam Yates, Primoz Roglic and Jakob Fuglsang, it looked like Lutsenko’s chances of winning the stage had evaporated.
But the 26-year-old had other ideas, launching into a sprint and holding on to take an emotional victory.
Adam Yates finished third to protect his overall lead in the race.
Speaking after the stage, he said: "The strongest guy won in the end, fair play to him."