The incident took place on PUSA Road near the Jassa Ram Hospital at around one AM yesterday.
The victim, identified as Jaspal Singh, a resident of west Delhi's Tilak Nagar, was beaten badly. Police have registered a case of attempt to culpable homicide.
Policemen Anand and Vikram, who were manning a police picket near the hospital, had rushed to the spot after they were told by a car driver that two men were beating up someone.
"The constables rushed to the spot and found two men beating up another man. They were yelling at him how he dared to hit their vehicle. They were also saying that will not leave him alive.
"When the constables intervened, one of them told the personnel that he was Raghav Gambhir and is the cousin of the cricketer (Gautam). The elder among them also told police that 'my son Gambhir is very powerful'," a senior police official said.
According to the official, the duo fled from the spot in their car while the policemen were trying to take the victim to a nearby hospital.
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A case under Sections 308 (attempt to culpable homicide), 506 (criminal intimidation) and 34 (common intention) of IPC.
No arrests have been made so far.
According to official statistics, 14 cases of road rage were reported in the capital this year till April 15 in which 20 people were arrested. One person was killed and 17 were injured in these incidents.
Last year, a total of 34 cases were reported and 49 were arrested. Two persons were killed and 35 injured in road rage incidents in the city.