Supergirl gets introduced in Ame-Comi Power Girl #3, and she has a ton of KO/sleepy scenes! First, she is discovered unconscious in a pod by Power Girl.
Afterwards, they are immediately attacked by robotic enemies of Braniac. Supergirl is placed in a green energy force field, which contains a sedative!
In Ame-Comi Supergirl #1, there's a really nice two page spread showing Supergirl drugged unconscious in these energy fields.
Powergirl manages to rescue Supergirl, and Supergirl mentions that she feels "Fuzzy".