The landing took place at 9:03 am. All 189 passengers and the crew members are safe.
All the 158 passengers on board, including crew, landed safely and will be accommodated on an alternate flight to their destination.
The victim Kailash Chandra Saini, 52, from Rajasthan, was accompanied by his 26-year-old son Heera Lal, reports the Khaleej Times.
An unverified video circulated on social media showing a graceful landing before the nose of the jet tipped over and ground to a halt.
The Sukhoi SSJ100 operated by national airline Aeroflot had 73 passengers and five crew members on board when it touched down and sped down a runway spewing huge flames and black smoke.
The flight was headed to Myanmar's capital city Yangon from Dubai.
The deceased was accompanied by one of his relatives to Bengaluru for treatment related to heart condition.
The pilot had to issue a 'May Day' call, made to seek help in times of distress, and the the Pratt & Whitney-powered Airbus A320 Neo plane landed at the Kolkata airport under full emergency conditions
The pilot had informed the air traffic control soon after the smoke alarm went off in the cockpit, the official said.
In a statement, Jet Airways spokesperson said, "Jet Airways is extending full cooperation to the DGCA for the ongoing investigation of the event.
Despite the twin snags and the scare, the 169 passengers on board unanimously applauded the stellar job performed by the two pilots on board.
A major engine vibration mid-air just minutes after take-off is said to have caused the emergency landing. It is yet to be verified what caused the vibrations.
The aircraft left for Bengaluru after a thorough inspection confirmed the warning to be 'spurious', the statement added.