Mrs Bennett said: "Previously the system has paid a benefit to these groups and then effectively left them to it. This is going to change."
And beginning in October, sole parents would have to be available for part-time work when their youngest child turned five, and full-time work when their child turned 14. At present, sole parents could stay on welfare until their children turned 18.
Women on the the widow's benefit and women alone benefit would also face these tougher work tests.
The bill was passed by 64 votes to 57, with National, the Maori Party, United Future and the Act Party in support and Labour, Greens, New Zealand First and Mana against.
Mrs Bennett said young people now faced greater obligation to work, but would have greater support in getting into education.
Someone on the Youth Payment benefit (previously the independent youth benefit) could earn $20 more a week by budgeting and staying in education. Someone on the Youth Parent Payment (previously the domestic purposes benefit or DPB) could earn $30 more a week.
They could also have their benefits cut if they failed these tasks.
After a budgeting expert helped them pay rent and bills, the remaining money would be placed on a payment card for use on groceries.
The reforms would be backed by $80 million in childcare support to encourage teen parents to remain in work.
Mrs Bennett, who claimed the DPB after having a child in her teens, said the changes did not show a lack of compassion: "I've a huge amount of respect for people who are raising their families with little money. I just want them to have more."
Labour's social development spokeswoman Jacinda Ardern said National's perception that welfare was a chosen "lifestyle" was misguided.
"We only need to look in our local areas where a job is advertised and the enormous queues which extend outside of ... supermarkets ... to know Kiwis want to work."
She added: "Changes in this area needed to reach all the young people whose potential is currently being wasted, not just a few, and they need to be based on getting the best outcomes, not just getting people off the books."
Ms Ardern felt the law focussed too narrowly on 16 and 17-year-olds who were not in education, work or training. People aged 16 and 17 made up just 14,000 of 80,000 young people on welfare.