Legislation giving the Government the power to set national literacy and numeracy standards has passed into law by 65 votes to 47.
Under the Education Amendment Bill, primary school children will have to be regularly tested and assessed against the standards.
It will also increase the maximum fine for parents of truant children from $600 to $3,000.
Labour and the Greens voted against the bill.
Parliament was debating on Saturday afternoon, under urgency, changes to the Sentencing Act, which will add guidance on legal consequences for offending against children.
Late on Saturday afternoon, a bill amending the Sentencing Act was passed into law with unanimous support.
The changes add guidance for courts on legal consequences for offending against children.
The Justice Minister, Simon Power, says the changes will be a step towards making the country's children safer.
Mr Power says it's important to get the legislation through before Christmas, because many children are especially vulnerable during that time.
The House has been sitting in urgency since Tuesday so the Government can pass a number of bills before Christmas.
Parliament sat until midnight on Friday, passing legislation making it easier for businesses with fewer than 20 staff to sack new employees within a probationary period of 90 days, and a bill amending the bail laws.
The House will rise until next week.
