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...

Captain America and Diamondback get knocked out while having a nice dinner at a restaurant. They wake up chained to a wall and in their respective costumes. Red Skull also "kills" Diamondback in this issue, but it turns out he just kills a cyborg version of her. I included that scene, but it's kind of violent....

In a scene that is way too brief, Black Mamba gets blasted unconscious by Nova.

In this manga about mech robots, a boy and girl couple get knocked unconscious early on. A big robot lands near them and blows them to the ground. There's a good unconscious and wake up scene involving the girl.

A girl faints and then has a gas mask apparatus placed over her mouth. Weird scene.

The Scarlet Witch battles the villain "Necrodamus", and is KOed. This scene is from Avengers, Volume 1, Issue #128 (Marvel, October 1974) Source: My Collection

Here is a Duo Damsel scene from "Superboy and the Legion of Super-Heroes", Volume 1, Issue #193 (DC, February 1973). She gets blasted out cold, plus there is a decent wake-up scene. I included more pages than just the KO because I thinks she looks really hot in this costume. Source: My Collection

From the pages of "Superboy and the Legion of Super-Heroes", Volume 1, Issue #207 (DC, March-April 1975) -- Light Lass gets karate-chop KOed, while Shrinking Violet is shown unconscious (the actual KO was, sadly, off-panel); but she looks really good getting tossed around by Superboy, who has been mind-controlled into ...

Cover art by Marat Mychaels.

Emp lies unconscious. Source: Comic

Not exactly a 'sleepy' sequence, although Deja is sound asleep at the start..I guess it would qualify as 'mind control peril'. Source: blog

Here are some scenes from Avengers #120-122 (February-April 1974) -- the Scarlet Witch and Mantis are KOed, and Wanda eventually exacts KO revenge on the villainess Virgo! Source: My Collection

Cavewoman is choked unconscious by another equally voluptuous woman. It looks like something Gytalf2000 commissioned :-) There's also a great alternate cover from Budd Root, which looks like an unconscious Cavewoman (or just really tired).

A young school girl faints outside, and a man in glasses carries her to a clinic where she is treated.

This scene from the August 1974 issue of the Avengers is a "gotcha" cover, since the Scarlet Witch was not KOed in the actual story. But she looks great in that unconscious pose in the Vision's arms! Source: My Collection

Lara has her hands and feet bound and is left to die in the desert. She's able to escape however. There's also a closeup of Lara for any who want it.

Spiderman(in his Stealth Suit)saves an unconscious Black Cat from a collapsing building.

The Scarlet Witch is felled by an energy discharge as she comes to the aid of the Vision. The Kree's Sentry captures her, and places her in bondage. a nice scene from the early 1970s! Source: My Collection

From a recent European comic. The cover shows a woman being dragged by her hair. The story starts with a girl waking up in a big spider's lair. The girl is bound with the sticky webbing. Supposedly she was KO'd in the previous issue by the bug, but we don't see it.

Amazing bondage cover showing Purgatori tied to a wooden stake and about to get burned!