An armed group, travelling in armoured vehicles, launched almost-simultaneous attacks on the prison and the municipal police station, Defence Minister Luis Crescencio Sandoval said in a news conference on Monday.
Authorities said the Sunday morning attack had coincided with preparations for New Year's Day visits.
They initially said the death toll was at least 14, but Sandoval said this had risen to 19 - 10 guards, seven prisoners and two attackers.
The attack allowed 25 inmates, including Ernesto Alfredo Pinon de la Cruz, also known as "El Neto", to escape.
Pinon is a top gunman for the Juarez-based "Los Mexicles" cartel, Security Minister Rosa Icela Rodriguez said at the news conference.
Federal authorities were called in to contain the unrest. They later found a "VIP zone" in the state-run prison with drugs and money, said Rodriguez, who slammed the Chihuahua state administration.
"That's the state's responsibility, because federal authorities can't intervene in these places," Rodriguez said.
She added that state authorities had not requested that any dangerous prisoners, such as "El Neto", be transferred from the overcrowded prison to a higher-security location.
State prosecutor Roberto Javier Duarte said in a separate news conference on Monday that state authorities would "completely clean out the penitentiary system" in response to the attack and that those guilty of corruption would be prosecuted.
The incident on Sunday resulted in one of the highest death tolls from prison attacks in Mexico in recent years.
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