Definitions:

1. To dull or deaden the senses or awareness, either physically or metaphorically. VERB
   • The narcotizing fumes from the paint rendered him unconscious within seconds.
2. To render insensible or unconscious, typically by administering drugs, particularly narcotics. VERB
   • The surgeon's precise injections of anesthetic had a narcotizing effect, rendering the patient insensible to pain.

Synonyms:

• anesthetizing
• deadening
• desensitizing
• drugging
• narcotic
• numbing