Bill Hader revealed in this interview that they pulled Mindy in during the live show...
“With James, he was originally in another sketch that got cut, so we just decided to stick him in ‘What Up With That,’ which started the whole visiting guest star thing,” he said. “Mindy Kaling we just grabbed on the way to the stage. She was just hanging out watching the show, and then she was sitting next to me asking me what to do.”
So that would be why Kristen didn't make it in the final sketch: