BERLIN, Vt. — It was a long way down for Michael Kenney. As he neared the depths of heroin addiction, he stole prescription painkillers from his dying father, replacing them with Tylenol and leaving his father writhing in pain.

But when Mr. Kenney, 39, a wiry man full of nervous energy, tired last year of living so many lies, the road back could not have been more daunting. He sought help at a clinic here, only to discover that there were 200 people ahead of him on a waiting list. It might be three months before he could receive treatment, he was told. He was so discouraged that he continued taking painkillers and shooting heroin.

Then the phone rang. It was the clinic.

In 2014, Gov. Peter Shumlin devoted his State of the State address to what he called a “full-blown heroin crisis” in Vermont. The State Legislature enacted many of his initiatives, including giving one-time grants to addiction clinics to help them reduce the size of their waiting lists. The Central Vermont Addiction Medicine clinic here used its share of the grant to extend the hours of its lone doctor. Counselors reached out to people on the waiting list, moving active needle-users like Mr. Kenney and pregnant women to the top.

Mr. Kenney says he is alive today because of the clinic’s sudden ability to treat him. He has been clean for several months now and has a full-time job at a gas station, answering roadside assistance calls. He lives with his wife and children and is preparing to open a bank account for the first time in his life.