Kovtun was strong throughout his flamenco-themed program, the only notable flaw that he was almost sitting on the landing of his second quad to keep his balance.
Machida, who won gold at Skate America, lamented that he was not in good condition in Moscow, but said it's not clear what's troubling him.
"Actually, I don't know," he said when asked about the specifics.
Fernandez, the European champion and world bronze medalist, expressed satisfaction despite his fall.
"I think I just had a little problem in the pattern and I just need to keep my mind clear," he said.
All four of the top women did triple-triple combinations. But Lipnitskaia landed a more difficult triple lutz-triple toe combo while Kostner, Zawadzki and Nagasu all did triple toe-triple toes.
In pairs, four-time world champions Aliona Savchenko and Robin Szolkowy led after the short program, followed by Russians Vera Bazarova and Yuri Larionov and Canada's Kirsten Moore-Towers and Dylan Moscovitch.
Ice dancers Ekaterina Bobrova and Dmitri Soloviev of Russia held a strong lead after the short dance, nearly seven points in front of Canada's Kaitlyn Weaver and Andrew Poje. Ekaterina Riazanova and Ilia Tkachenko of Russia were in third place.
Lipnitskaia, who won gold at Skate Canada, will qualify for the Grand Prix final with a medal of any shade in Moscow. Kostner would qualify with a gold, but Zawadzki, after a seventh-place finish in the Cup of China, is out of contention. The top six skaters in each discipline qualify for the final, which is Dec. 5-8 in Fukuoka, Japan.
Lipnitskaia's program began on a mysterious note, with her crouched down and drawing figures with her finger on the ice. Asked what that's all about, she chose to keep the meaning hidden.
"Everyone can see what he wants to," she said.
But once she rose from the crouch, the 2012 junior world champion's program was crystal-clear: a clean triple-triple, a precisely landed double axel and a very fast combination spin at the end.
The veteran Kostner, who said she is contemplating retirement after the season, said she was soothed by being back on the ice at Moscow's Luzhniki Small Arena. The arena was the practice rink for the 2005 world championships, where she won her first world medal, a bronze.
"It feels very special," Kostner said. "It's funny to see so much time has passed."
The top pairs all struggled, notably Savchenko's hard fall on a throw triple axel, a challenging move that the pair daringly puts almost at the end of their program when their energy has flagged somewhat.
"It's a risky element," Szolkowy acknowledged. "We tried it in several positions; we found at the end it is best."
Bazarova put her hand down on the pair's opening triple toe loop and landed awkwardly on the throw triple loop, but said it was all an improvement over last week's Trophee Bompard, where the pair was fourth.
"Today, we got the maximum levels," she said.
Moscovitch took his fall in stride, saying, "I was working on some yoga positions on the landing."