Hoelgaard (Uno-X Norwegian Development Team) beat compatriot Amund Grøndahl Jansen (Jumbo-Visma) to make it a home country one-two as Lutsenko (Astana) and Barguil (Arkea-Samsic) battled for the overall.
"I am so happy with this victory," Lutsenko said of his first victory as Kazakh champion. "It is an amazing feeling to fight until the last meter and to win.
"I had huge support from my team, and I want to thank all teammates for this week and for this victory. It is our team’s success."
The punchy 165.5km stage from Lødingen to Narvik was always going to be sensational and it did not disappoint with the action kicking 50km out from the finish.
A nine-rider group was up the road as Astana) and Arkea-Samsic pulled the peloton along in its wake, keeping the race under control.
The break split into four as intermediate points were chased but with less than 30km left to race the entire peloton was back together. Along the way, Stage 3 winner Odd Christian Eiking (Wanty-Gobert) secured his King of the Mountains salmon jersey, taking the points on offer.
The last intermediate sprint - with 10km of road left - went to Lutsenko ahead of Barguil before Hoelgaard went clear in the last climb.
As the stage reached its conclusion, Grøndahl Jansen tried to bridge to Hoelgaard but fell short in the final kilometre while Lutsenko grabbed the opportunity to take third and the four seconds bonus, bringing him level with Barguil, with the single second on the line between them the final difference.
"Yesterday we had a super hard stage and the final climb did not suit me really well, but I knew that today’s profile would suit me much better," Lutsenko said. "So, I was motivated to do something, and I succeed.
"I knew I had to attack on the local laps, and I did my best. I attacked for many times, but every time Barguil was on my wheel. He did a great race too. It was hard to drop him on the last climb, so I put everything on the final sprint and this tactic worked out very well."
Highlights and replay to come.