Lutsenko attacked from the gun and dominated his breakaway companions for a brilliant solo win ahead of Merhawi Kudus (Dimension Data). Marc Soler of Movistar rounded out the stage podium places.
Though he is no longer a the GC contender, Alberto Contador (Trek-Segafredo) was the first of the big names to the summit, just ahead of Chris Froome (Sky), who retains the red jersey.
"In 2014 I did my first Vuelta and managed to get a second place, but this is the biggest win of my career, no doubt," Lutsenko said.
"It was very hard before the final climb and we were a bit alone out there. Into the headwind, we knew it would be tough, especially with lots of guys chasing behind. In the end, it was a great stage for me, and I want to thank my teammates."
Team Sky's Froome has a 10-second advantage on US rider Tejay Van Garderen and Orica-Scott's Esteban Chaves looked impressive to move into third place overall at 11 seconds.
Froome was set up by team-mate Gianni Moscon, with Contador matching his pace despite suffering recent stomach problems.
"My sensations were better than they have been for the past few days, and I'm pretty happy with how it went. We still have quite a bit of work to do," Contador said.
"I'm reasonably happy with how it is going. The crowd was really impressive and I'm happy that I could do something for them."
The 17 other riders in the Lutsenko break were kept under control by Sky, with the gap hovering between 3min 30sec and 4min 30sec for most of the stage. At the front, Davide Villella (Cannondale-Drapac) dominated the four first climbs of the day to extend his lead in the KOM classification.
The dynamics of the stage changed in the final 45km, following an attack from the break by Katusha-Alpecin's Marco Haller. Lutsenko was the lone responder with 33km to go and the following battle shattered the leading group while the gap with the peloton doubled as the race entered the final 20km.
Lutsenko then unleashed his raw power to drop Haller in the final climb and cap his brilliant ride with a solo victory.
Behind, as Contador and Froome kicked on, only Michael Woods (Cannondale-Drapac) and Chaves could follow them while Vincenzo Nibali (Bahrain-Merida) lost 26 seconds and Romain Bardet (AG2R-La Mondiale) 49.
Orica-Scott rider Jack Haig was 25th on stage five and remains the best-placed Australian at 18th overall. One significant abandon was Trek-Segafredo's John Degenkolb, forced out due to bronchitis.