People.com said the couple were doing the rumba to "Over the Rainbow" when Chmerkovskiy's leg collapsed and he and Alley fell to the floor.
They quickly recovered and completed the routine.
"My thigh just gave out. I'm so sorry. I'm so sorry," Chmerkovskiy said later. "It has nothing to do with her."
The judges awarded them 21 out of 30 points and praised them for their fortitude, People.com said.
"You've overcome it," said judge Len Goodman. "You got up and dusted yourself off."
"You can't keep good talent down. Once you got up it was better than ever," added Bruno Tonioli.
Alley is best known for her work in the sitcom "Cheers," as well as the "Look Who's Talking" series of films.