Slovenian skier Kranjek posted a significant advantage ahead of the two Norwegians.
Henrik Kristofferson finished second, 0.60 seconds behind Kranjek, and Lukas Brathen 0.73 behind third.
Odermatt, who appeared tired after several days of downhill racing in Val Gardena, later scored a 1.42 in the second stage on the Gran Risa course.
Kranjc overtook Brathen at the final checkpoint, but made up time on the flatter lower course.
At the Beijing Olympics last winter, Kranjc was the only racer to seriously challenge Odermatt, who won gold amid a blizzard.
Odermatt won two giant slaloms early in the season, while Kranjek finished second and third in Sölden, Austria, and Val d’Isère, France, respectively.
Nevertheless, Odermatt could extend his lead in the overall category after Alexander Amodt Kilde, who is second in the standings, did not complete his run.
Kranjc is chasing his third World Cup victory, which would match Jure Kosir, bronze medalist in slalom at the 1994 Olympics, the most by a Slovenian man.
Radamus River and Tommy Ford, the top American GS skier, both had trouble.
Radamus, who finished fourth at the Olympics, fell on his left hip on the uppercut and did not finish. Ford also lost control and had to calibrate his skis to make the next gate, eventually falling behind by about 5 seconds.
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