24-year-old Akash Ananth on a solo flight missed the Cheltenham East Primary School by just 60 metres as his plane, caught in a mid-air collision, plummeted to earth.
The Cessna exploded at the back of a block of units opposite the school, where 220 students were on a lunch break.
The pilot, 24-year-old Akash Ananth, died on impact, but may have saved dozens of lives by guiding the plane away from the school grounds.
Another student pilot, also Indian, and his instructor in the second plane managed to return to Moorabbin airport.
Both trainee pilots were learning to fly with the Royal Victorian Aero Club.
Language difficulties between the Indian students and the air traffic control tower have been identified as a possible cause of the tragedy.
"We were very lucky that the pilot's skill allowed him to land the aircraft where he did," a Metropolitan Fire Brigade spokeswoman said.
"Had he crashed across the road, he would have gone straight into the primary school.
"He managed to land the aircraft in such a way as to protect the public.
"He was a bit of a hero."
The dead pilot, an Indian national from Bangalore in southern India, arrived in Australia two months ago and was staying with his cousin, Dilip Mysore, and his family in Clayton South.
Mysore said his cousin had been flying for nearly two months and had done his first solo flight last Saturday.
Ananth had been studying to be a pilot in Bangalore, India, for about a year before arriving in Australia two months ago on a student visa.
"He had plans of going to France and flying for Airbus or Boeing," Mysore said.
"He liked everything about Melbourne except the cold.
"He was a pretty social guy and got along well with everyone," Mysore said.
The flying school has many Indian students, and several went to the crash scene soon after the tragedy.
Student pilot Ben Zachariah said he did not know Ananth but was told he was on a solo flight.
"He was forced to do a spiral dive. He would have been doing circuits, which means you are not more than 1000 feet high, and couldn't have had time to do it safely," Mr Zachariah said.
Police said Ananth's parents in India had been told of the tragedy.
The crash sparked fresh calls for Moorabbin airport to reduce the volume of air traffic.
"This is not a safe environment for people living here," said Tom Uren, of Moorabbin Airport Residents Association.
"We've been waiting for this to happen.
"It chilled my blood when I heard about it.
"We are extremely lucky there was only one death.
"It could have been a terrible disaster."
Both aircraft have been in service for more than 30 years.
Civil Aviation Safety Authority spokesman Peter Gibson said they were among the most popular training planes in the country.
"Local residents shouldn't be concerned about these sort of things happening frequently. They don't," he said.