TIJUANA, Mexico  The sedated patient, his bullet wounds still fresh from a shootout the night before, was lying on a gurney in the intensive care unit of a prestigious private hospital here late last month with intravenous fluids dripping into his arm. Suddenly, steel-faced gunmen barged in and filled him with even more bullets. This time, he was dead for sure.

Hit men pursuing rivals into intensive care units and emergency rooms. Shootouts in lobbies and corridors. Doctors kidnapped and held for ransom, or threatened with death if a wounded gunman dies under their care. With alarming speed, Mexico’s violent drug war is finding its way into the seeming sanctuary of the nation’s hospitals, shaking the health care system and leaving workers fearing for their lives while trying to save the lives of others.

“Remember that hospital scene from ‘The Godfather?’ ” asked Dr. Héctor Rico, an otolaryngologist here, speaking about the part in which Michael Corleone saves his hospitalized father from a hit squad. “That’s how we live.”

An explosion of violence connected with Mexico’s powerful drug cartels has left more than 5,000 people dead so far this year, nearly twice the figure from the year before, according to unofficial tallies by Mexican newspapers. The border region of the United States and Mexico, critical to the cartels’ trafficking operation, has been the most violent turf of all, with 60 percent of all killings in the country last month occurring in the states of Chihuahua and Baja California, the government says. And it has raised fears that violence could spill across the border, because dozens of victims of drug violence have been treated at an El Paso hospital in the last year.