Mr Dunne, who made his comments in a speech to a new group established to address opioid harm, said hospital systems may create circumstances that increase the chance of harm.
This included when patient care was transferred between different health services.
"Recently an 82-year-old patient with kidney impairment was prescribed high-dose oxycodone to take home.
"Very sadly, two days later they were found unresponsive in their home, and then died due to complications associated with opioid toxicity."
The Health Quality & Safety Commission has partnered with district health boards in a national opioid collaborative from October last year to April 2016.
Mr Dunne addressed the collaborative at Te Papa, Wellington today, and said the immediate priority was the high rate of opioid-related harm identified in New Zealand hospitals.
"The challenge for you is to test interventions, and to identify the ones that demonstrate proven reductions in opioid-related harm, which can then be shared nationally."