The silver car was destroyed after crashing through the wall of the cemetery.
It happened in the early hours of this morning in Lindley, Huddersfield.
Officers from the Roads Policing Unit said the drink driver was "lucky not to have ended up in one of the graves."
They said: "This drink driver in Lindley is lucky not to have ended up in one of the graves they've just destroyed."
The drink-driving limit for drivers in England, Wales and Northern Ireland is 80 milligrams of alcohol per 100 millilitres of blood, 35 micrograms per 100 millilitres of breath or 107 milligrams per 100 millilitres of urine.