Russia's defending Olympic champion Kriukov edged out Petter Northug to win the men's event.
Kriukov and Dmitriy Japarov went out quickly in the final but 2009/2010 World Cup champion Northug looked to have made a decisive move on the final climb.
But Kriukov got in Northug's slipstream and beat him in the dash to the line by four tenths to end Norway's World Cup winning streak this season at five races.
Kriukov said: "I am very happy. I knew that Petter was very strong uphill but the last 100m I tried my best to win."
Eirik Brandsdal was a distant third ahead of Japarov with Alexey Poltoranin and Kalle Lassilan taking the minor places.
Leading qualifier Emil Jönsson crashed out in the opening semi while defending discipline champion and Swedish team-mate Teodor Peterson was fourth in the same race and did not progress to the showpiece.
Norway's Bjorgen followed up her victory in Saturday 10km event in Gällivare with an emphatic victory in the women's event.
The defending World Cup champion finished two seconds clear of Russia's Evgenia Shapovalova whose compatriot Anastasia Dotsenko took third.
The triple Olympic gold medallist made a slow start in the final but a stumble by early leader Katja Visnar of Slovenia delayed her and Krista Lahteenmäki.
Bjorgen, who only reached the semi-finals as a lucky loser, then surged ahead on the final uphill climb to claim her 57th World Cup victory.
Bjoergen admitted her change after the heats made all the difference, saying: "I felt better and better as the races went on and I am really happy to have won.
"I changed my skis after the first race and a little bit of my technique because they weren't that good for the heats but I was happy with the semi-final and final."
Anne Kylloenen of Sweden was fourth ahead of home favourite Lahteenmäki and Visnar.
Bjorgen's main rival Justyna Kowalczyk was the top qualifier but came only third in the opening semi-final and did not progress as a fastest loser, nor did defending World Cup discipline champion Kikkan Randall.
- Sports & Recreation
- Athletics, Track & Field
- Petter Northug