I still maintain that Elena winning her fight made no sense, however. Katherine was able to hold at bay both Damon and Stefan after being staked, no way Elena can overpower her.
Although there are enough plot-holes this season that fanwanking explanations for all of them would required a near religious devotion, I can get past this one (if not Elena and Jermey taking on Kol). The only explanation for Elena being alive at all is Kat not really wanting her dead.
It's not that unreasonable. Katherine is self-serving and all about survival, but she isn't generally unnecessarily homicidal. And, though she clearly finds Elena irritating and useless, she doesn't really have a reason to kill her. Plus, Kat may well view her as sort of distant family, all she has left. Or just find it weird to actually kill her double.
In any case, if Kat doesn't want her dead, then she may not be fighting harder than necessary to prevent Elena from succeeding, which baby-vamp to half-millennial is probably not very hard. But being Katherine, she's pissed enough to still knock the shit out of her and kill her if it comes to it.