A.C.
Yep. After you finish nursing at night when your baby is asleep, wake her up again gently so that her eyes are open when you put her down to bed. You don't have to stop nursing at night to stop nursing her to sleep. Eventually (it didn't take my son long at all), she'll figure out that falling asleep during nursing doesn't pay off.
If that doesn't work, my friend used to take steps to keep her son awake during nursing, such as keeping a cool cloth next to her and gently wiping it across her son's neck or feet when he started to drift so that he was awake when he finished. Then she put him down, tired but awake. You could try whichever technique is more suited to your baby's personality.
Good luck.