The first time Connie the Hormone Monstress takes the screen in “Big Mouth,” she takes it over completely. She emerges from the shadows in a flash of lightning, as if zapped to Earth by some vengeful, horny god. As she takes in her new charge, a tiny redhead scared to death of her changing body, she grins wide enough to show her pointed teeth. Connie is a feat of smart animation before she says a word — but it’s once she opens her mouth and Maya Rudolph’s voice comes out that Connie becomes truly unforgettable.

It’s wild that “the Hormone Monstress” is the character who’s finally won Rudolph her first Emmy, but if you’ve seen even a minute of this performance, it isn’t shocking. Rudolph’s Hormone Monstress was a game-changer for “Big Mouth.” On a narrative level, her total commitment to the part ensured that Connie,...