Kriukov saw the six-strong classic sprint final in Asiago effectively become a contest between four with Emil Joensson going down and taking out Alexander Panzhinskiy just over halfway in.
And he produced the perfect finish to claim the first World Cup win of his career, Kriukov getting the better of Poltoranin of Kazakhstan by 0.14 seconds with his winning time 4:21.18minutes.
Gianluca Cologna of Switzerland strolled home 4.11 behind in total for third and Russian Kriukov, who won the Olympic sprint title at Vancouver 2010, couldn't hide his delight.
He said: "I am very happy. I have had a long wait for victory in the World Cup and I did it. I am so happy. It is unbelievable. I love Italy."
In contrast Kowalczyk has now won all four classic World Cup races to have been staged this season after clocking 3:14.03 for a comfortable victory over Anne Kylloenen.
Kylloenen battled but finished 1.34 behind with Maiken Caspersen Falla third and Kowalczyk revealing she'll now enjoy Christmas before the start of the Tour de Ski.
Kowalczyk will therefore not race in the team sprint next in Asiago and she said: "I like the classic, my classic is good and I am very satisfied. It is Christmas now."