chasing them in the early hours of Friday, Watertown's police chief Edward Devau told CNN.
Tamerlan Tsarnaev, 26, died in the shootout while his brother, 19, eluded capture until late Friday, when he was found hiding in a boat in Watertown.
Devau told how Dzhokhar ran over his brother, dragging the body down the street as he escaped from police, who had trapped the older brother.
The suspects were involved in the killing of a police officer at Massachusetts Institute of Technology and then stole a Mercedes, sparking a chase to Watertown, in the Boston suburbs, according to the police account.
Devau said two off-duty police were helping four officers who confronted the brothers in the overnight shootout.
"We estimate that over 200 shots were fired over a five-to-10 minute period," Devau said, adding that the brothers also hurled a pressure cooker bomb and other homemade explosives.
"We found a pressure cooker embedded in a car down the street" after it caused "a major explosion during this gunfight," Devau said.
Two homemade grenades exploded and two others failed to go off. Another device was found in an abandoned car, he said.
Devau told how Tamerlan Tsarnaev suddenly emerged "and just starts walking down the street shooting at our police officers trying to get closer."
When the suspected bomber ran out of ammunition, two or three police overpowered him and were trying to handcuff him when the other brother drove the carjacked black Mercedes at them, said the police chief.
"One of them yells 'look out," said Devau. "They dive out of the way and he runs over his brother and drags him a short distance down the street."
Doctors officially pronounced Tamerlan dead at the hospital, where his brother is now being treated.
Dzhokhar drove off amid more gunfire, but two or three streets down, "he dumps the car and runs into the darkness in the streets. Then we lost contact with him," said Devau.
Dzhokhar Tsarnaev was eventually cornered, wounded and hiding in a boat that was being stored in someone's backyard. Devau said that the suspect made no statement at the scene.