CULIACÁN, Mexico—At a half-built house in a barrio, a longtime Sinaloa cartel employee used a shovel to mix chemicals in a simmering oil barrel.

His concoction was an illegal form of fentanyl, which Mexican criminal organizations are churning out at high volume in laboratories and smuggling across the border. In a six-day workweek, the cook said, he can make enough fentanyl for hundreds of thousands of doses.