The parents argued their children's lungs were not yet developed enough to handle the increasing pollution in the city.
Delhi, with 16 million people, is one of the world's most polluted cities.
In recent years it has got noticeably worse around Diwali, when huge quantities of fireworks are set off.
On Friday, the Supreme Court suspended the "possession, stocking and selling" of fireworks in Delhi and its neighbouring suburbs "until further orders".
The court also directed pollution control authorities to "study harmful effects of materials used in firecrackers in three months".
The ban has been welcomed by Gopal Sankaranarayanan, the lawyer representing the three sets of parents, who pointed to the rise in pollution following October's celebration.
"This year, shortly after Diwali season was over, we had the worst instance of pollution in 20 years," he told the BBC. "It was pretty bad in the 10 days to two weeks following Diwali."
In fact, pollution in Delhi increased to nearly 10 times the safe level after Diwali, the most important Hindu festival in north India. causing panic and outrage.
Residents awoke from a night of colourful fireworks to find the city covered in a thick grey blanket of smog.
There have been several campaigns in the past asking people to use fewer fireworks during the festival, but these have not met with much success.
Despite the victory, Mr Sankaranarayanan was critical of the government's response to date, pointing out that other countries have tackled the pollution issue head-on.
"The first step in any of this is a source apportionment study over a 12-month period so you know exactly what is causing the highest levels of pollution over the year," he said.
"China did it when it was facing problems, Indonesia did it, Dubai does it - but we don't. And still to date, despite [Delhi] being called the most polluted city in the world, the government has not commissioned a source appointment study."