This could be an ambush predator of the type that digs a burrow and lies in wait of its prey. Something like an antlion. The predator has a pit that acts as a trap and while it lies in wait it exhales carbon dioxide into the trap. CO2 being heavier than air it will accumulate in the pit.
The prey species drops into the gas-filled trap and provided the air-CO2 mix is right or close enough this will act as an aesthetic gas. The prey will be anaesthetized and falls 'asleep'. Next thing it's munchies time. Good for the predator, but not so good for the prey.
Most probably this form of predation will only work with small organisms. Creatures the size of spiders and ants, and similar. However, old mine shafts do tend to accumulate CO2 and this can be fatal for the unwary. Perhaps, if the environment is right and if the predator can dig its trap deep enough to connect with underground fissures then this might provide a natural source of CO2. So larger predators and prey using Co2 anaesthesia might be larger organisms.
With humans 30% CO2 mixed with 70% oxygen results in intoxication leading to unconsciousness. See here. This suggests that if a predator can set a trap filled with enough CO2 it might anaesthetize its prey. While this isn't exactly inducing sleep in its prey anaesthesia is the next best thing.