Filmed by a passenger on board one of the planes, the footage shows one plane pass directly under the other as both were forced to abandon their landings.
The Emirates plane was cleared for take-off and began to head down the runway. As it gathered speed, a Qantas plane appeared on the radar behind it, ready to land on the same runway.
A second Qantas aircraft was approaching from the right.
To avoid a collision both Qantas pilots aborted their landings.
The planes were said to pass less than 1852 metres apart.
One of the planes also breached the minimum altitude distance above the terminal.
Senator Nick Xenophon said a "series of systematic failures" led to the near miss.
While many airports have parallel runways, Melbourne has intersection runways. A set-up criticised by safety analysts.
In a statement, Airservices Australia said there was never a threat to passenger safety during the incident.
