The rod was lying on a construction site when the taxi Supratim Dutta was travelling in smashed into it Thursday.
The 60-centimetre-wide (two-feet) bar crashed through the car's bonnet and dashboard before hitting the 23-year-old, who was sitting in the car's front passenger seat.
Despite the incident, he remained conscious and called family and friends from his mobile phone while he waited at the scene for an hour before being taken to hospital, newspapers reported.
Indian media described the three-hour-long surgery as a miracle after the iron bar, weighing six kilograms (13.2 pounds), cut through his liver, stomach, spleen and left lung.
It also perforated the man's diaphragm in two places and broke a rib, but missed his heart, The Times of India reported.
"In my 35-year long career, this is the first time that I have seen a case like this," the newspaper quoted doctor M.C Misra as saying.
Doctors at the premier All India Institute of Medical Sciences said the surgery was difficult as the rod's angle prevented doctors from establishing the extent of internal damage.
Three of Dutta's ribs had to be cut to free the rod from his body.
Doctors said he was in a stable condition, but post-surgery infection could pose a danger to his life.