Faced with an unrelenting epidemic of heroin and pain-pill deaths, many states are pushing to make more widely available a drug called naloxone that can reverse overdoses from such opioid drugs within minutes.

In North Carolina, Louise Vincent, an outreach worker in Greensboro, has rescued scores of opioid addicts from the brink of death by giving them naloxone.

Now, she is delivering the drug to those she says are in the best position to help overdose victims—their friends and family members—under a North Carolina law passed last year that expanded access to naloxone.

"It could be the difference between life and death," said Ms. Vincent, a contract worker for the North Carolina Harm Reduction Coalition, a not-for-profit organization that has dispensed about 3,000 naloxone kits statewide since the law took effect.

The program so far has resulted in 125 overdose reversals, said Executive Director Robert Childs. Deaths from heroin and pain medications totaled 712 in North Carolina in 2012, according to the state's Department of Health and Human Services.