But for adults there is still disparity in wages and Maori are more likely to be on a benefit.
Gaps between New Zealand's main ethnic groups are closing for our youngest citizens - but remain deeply entrenched on many indicators for older children and adults.
A major Herald investigation, including data from last year's Census, has found ethnic gaps have almost disappeared in the past two years for infant mortality and may close within the next few years for children attending preschool education.
Traditionally disadvantaged Maori and Pacific people are also catching up with Europeans and Asians on most other health and educational measures and in occupational structure, thanks to a burgeoning brown middle class.
However, Maori and Pacific average incomes are not catching up, their employment rates have dropped more than Asians and Europeans in the recent recession and more Maori and Pacific children are being hospitalised with poverty-related illnesses.
Former Children's Commissioner Dr Cindy Kiro, now head of Maori education at Victoria University, said the gains for the youngest children were "a cause for celebration".
"I'm mindful of how much effort has gone into that, particularly through community and primary healthcare and things like immunisation and lowering the rate of Maori sudden infant death syndrome," she said.
More than 90 per cent of children in all main ethnic groups, except Pacific children, attend early childhood education before starting school. Even the Pacific rate rose from 87.4 per cent in 2012 to 89.3 per cent last year, so it looks likely to exceed 90 per cent this year.
Otago University economist Dr Simon Chapple said Maori and Pacific educational attainment at school and tertiary levels had rocketed since the 1970s, creating a growing middle class.
He said there were only 170 Maori people with degrees in 1971. By last year's Census there were 36,075.
However, the average earnings gap between Maori and European hourly wages has been stuck at around 17 or 18 per cent for the past decade, and Maori have become even more likely than Europeans to be on welfare benefits in each Census year since 2001.
Dr Kiro said the country was still ignoring the best opportunities to close the gaps in the labour market, such as higher subsidies for apprenticeships and more income support and social housing for low-income families.
State of ethnic gaps
Gaps that are closing
* Infant mortality - gaps almost closed.
* School leavers with NCEA - gaps may close in 10 years.
* Early childhood education - gaps may close in 11-13 years.
* Life expectancy - gaps may close in 45 years.
* Adults with degrees - gaps may close in 40-80 years.
* Occupational structure - gaps may close in 60-90 years.
Gaps that are barely budging
* Imprisonment rate - gaps may close in 1170 years.
* Gaps that are not budging
* Average hourly wages.
Gaps that are widening
* Children hospitalised with diseases of poverty.
* Partnership status.
* Home ownership.
* Welfare dependency.
* Child abuse.
* Violent offending.