JESS: You’re definitely broken up with Dean?
RORY: Yeah, I’m definitely broken up with Dean.
JESS: Okay. I have to go take care of something then.
Before anything happens between Rory and Jess, he leaves to break up with Shane. It’s six in the morning and she’s been stuck watching a dance marathon for eighteen hours – let the poor girl get some sleep, Jess! However, it does show that Jess has a responsible side, and is not going to cheat on Shane, no matter how badly he treated her otherwise.
The Annotated Gilmore Girls 