ASUNCIÓN, Paraguay — At least 75 members of a powerful Brazilian drug cartel escaped from a prison in northern Paraguay through a tunnel on Sunday, pulling off an escape plan that officials had known about for more than a month but were unable to stop.

The breach is the latest and most serious sign that Brazilian cartels, which use Paraguay as a transit point to smuggle arms and drugs into Brazil, have penetrated the security agencies.

“This is a prison break without precedent,” Paraguay’s justice minister, Cecilia Pérez, said on Sunday. “This is the biggest prison break from our facilities.”

Members of the cartel, the First Capital Command, had spent weeks digging the tunnel from their wing of the Pedro Juan Caballero prison, piling dozens of bags of dirt into a cell, according to officials in Paraguay.