Right before Gothel's fall, Rapunzel reaches out trying to save her. I've probably spent more time thinking about that scene than I did explaining to my wife how those frilly Tangled panties got into my underwear drawer. See, for most of the movie, Rapunzel did not see Gothel as a villain. She saw Gothel as her mother, a person who has cared for her since she was an infant -- and that's what makes Gothel so evil.
She wasn't your typical Disney villain. She had no magic powers or an army of evil minions. All she had was the complete control over one person, and she used it to make her kidnapped/adopted (kidopted? adoptnapped?) child love her. So, even after Rapunzel saw Gothel kill the guy she fell for, she still didn't want Gothel to die. That's why Rapunzel reached out to save her. It might have been because of the overwhelming power of filial love, or it might have been due to severe Stockholm syndrome. In any case, that is A LOT of drama to squeeze into a half-second, and a definite step-up from the original story about a kid named after fucking salad.