Bjoergen executed the perfect race in the women's cross country skiing sprint classic final, making her move at the halfway stage to win her third world sprint gold medal and sixth individual one in total.
Kriukov, the Olympic sprint champion, meanwhile made a telling move with metres to go of the men's final to deny Petter Northug and a Norwegian double.
Bjoergen won four golds and a silver at the last Nordic World Ski Championships on home soil in Oslo in 2011 but is refusing to get ahead of herself after just one event in Val di Fiemme.
"It is too early to say. I am really happy and it seems that my shape is good," said Bjoergen, who finished second in the last World Cup sprint race before the World Championships.
"It is a good start and it means a lot for me. I am looking forward to the rest of the event and we will see.
"I am very satisfied with that. I thought the sprint would be hard for me after my last race in Davos where I didn't feel good.
"I wondered how my shape was but my skiing was perfect and the guys in the waxing cabins did a good job and I am very happy."
Meanwhile Kriukov admitted his performance in Val di Fiemme was up there with his one in Vancouver three years ago where he claimed Olympic sprint gold.
"This is the second time that I win but it was harder than the first one. The first one was the Olympics and this is a great start," said Kriukov.
"I am very happy. It was amazing racing and the Italian people are very friendly and I like it. Last time in Canada I liked it and I like Canada and Italy.
"Tactically I wanted to push the last uphill and have a strong finish. I knew Emil [Joensson] and Petter would be very fast and I wanted a good last uphill and finish."
Bjoergen found herself at the back of the pack in the final following the start with Maiken Caspersen Falla and Katja Visnar battling for contention at the front early on.
Drama then ensued ahead of the climb with Justyna Kowalczyk getting her ski pole clipped on Stina Nilsson's and falling to the ground.
With Kowalczyk now out of the race, Falla still led at the halfway stage however Bjoergen was now right behind her along with Ida Ingemarsdotter of Sweden.
Bjoergen then made her move and was perfect on the final left-hand corner, extending away from Ingemarsdotter to take the win.
She clocked 3:16.6minutes for the win with Ingemarsdotter 2.3seconds away in second while Falla had to settle for bronze 3.7 behind in total.
Meanwhile in the men's final Emil Joensson and Kriukov raced to the front early on with the Olympic champion dropping back to third after the halfway stage.
Joensson and Northug took control however a burst of speed on the last uphill promoted Kriukov to first and had the quicker sprint at the finish.
He crossed home first 3:30.4 with Northug unable to catch him and finishing just 0.3 behind while Canadian Alex Harvey come from nowhere to take bronze a further 0.5 adrift.