Labour, the Greens and NZ First opposed the bill.
Labour MP Poto Williams said it was her party's firm view that vetting was a core service of Police. The Government needed to increase funding to Police so they could comfortably cope with vetting requests, she said.
"We feel that police vetting is like the first line of defence ... we are also sad that this does lead us down the slippery slope of being able to charge for other activities within the police range of activities. And that is not appropriate."
Police Minister Judith Collins said New Zealand Police was one of the few police services in the world that could not claw back some costs.
The vetting service faced sky-rocketing demand, she said, that had increased by more than 100,000 vets per year since 2012/13. That growth was forecast to continue.
The law change will allow Police to recover more than $3 million each year.