American Mirai Nagasu took bronze.
In pairs, Aliona Savchenko and Robin Szolkowy of Germany won gold, followed by Russians Vera Bazarova and Yuri Larionov and Canada's Kirsten Moore-Towers and Dylan Moscovitch.
Lipnitskaia also won Skate Canada, and her second victory of the season means she qualified for the Grand Prix Final which she missed last year due to injury. Kostner and Nagasu won't make the final.
"I'm happy to qualify for the final with two victories, but I'm very dissatisfied with today. It was most likely my worst performance ever in competition," she said. "I made a mistake on the first jump and wasn't able to pull myself together."
Lipnitskaia was well ahead of Kostner going into the free skate after a precise and ambitious short program. But after falling on her triple lutz, she put her hand down on the second jump. Kostner opened well, but later put her hands down on two jumps. She won the free skate, but ended 0.68 points behind Lipnitskaia in the overall results.
Kostner, a 26-year-old veteran and the 2012 world champion, took it in stride, saying she won't let it distract her from preparing for the Sochi Olympics.
"I made a few mistakes, but that's how it goes building up to an important event," the Italian said.
Nagasu was pleased with third, after her eighth-place finish at the NHK Trophy.
"I wish I could put two and two together and make it to the final, but unfortunately that isn't the case. I'll take it as a blessing in disguise because then I have more time to train for nationals," she said.
Nagasu had been in fourth, just one-hundredth of a point behind compatriot Agnes Zawadzki, whose troubled free program landed her in sixth place overall.
Savchenko took a hard fall in the short program, but showed no signs of lasting trouble in the pair's program to The Nutcracker Suite, which ended dramatically with a throw triple salchow as the music climaxed.
Tchaikovsky is always a hit with Russian crowds and Savchenko said she was a bit nonplussed when the crowd started clapping at the early notes.
"I thought it was really nice, but I also thought maybe we'd missed something," she said.
The German and Canadian pairs qualify for the Grand Prix Final, but Bazarova and Larionov, after a fourth-place finish at Trophee Bompard, won't go.
Moore-Towers fell on her chest coming out of a lasso lift, which she casually characterized as one of "a couple of little weird things" in the routine.
"We forgot to land a couple of things," Moscovitch said, laughing.