A single officer was first to encounter the fugitives at 12.30am local time on Friday in a residential street in Watertown, a suburb of Boston.
They were in two separate vehicles, including a four-wheel-drive Mercedes they had carjacked.
Chief Deveau said: “They jump out of the cars and unload on our police officer. They both came out shooting. Shooting guns, handguns. He’s under direct fire, very close by.
“He has to jam it in reverse and try to get himself a little distance.”
As five other officers arrived, 200 shots were fired in 10 minutes. One of the brothers threw exploding devices including a pressure cooker bomb which landed on a car.
Tamerlan then broke cover and walked directly at officers firing a gun. The police chief said: “They were having a gunfight 10 feet apart. And then for us, thank God, he ran out of ammunition. He runs out of ammunition, the bad guy, and so one of my police officers comes off the side and tackles him in the street.”
As they tried to handcuff him, Dzhokhar drove the Mercedes straight at them but missed the police, hitting his own brother and dragging him 20ft before racing off.
Chief Deveau said: “The officers dive out of the way and he (Dzhokhar) drives over his brother and drags him a short distance down the street.”
Doctors said Tamerlan had injuries “head to toe”. There were so many they did not know which one had killed him.
The brothers were found to have had six improvised explosive devices including a satchel bomb, handguns, a rifle, 250 rounds of ammunition, and home-made grenades.
Dzhokhar dumped the Mercedes a few streets away.
Nineteen hours later, he was found bloodied and hiding underneath a tarpaulin in the boat in the back yard of David Henneberry’s home.
Stark images from a thermal imaging camera on a helicopter showed him lying inside the boat. Police used a robot to remove the tarpaulin and threw in flash bombs.
A negotiator on the second floor of the house, looking down on the boat, successfully talked Dzhokhar out after 30 minutes.
Over the weekend, it emerged that Tamerlan was married to Katherine Russell, 24, whose family lives in an upper middle-class neighbourhood in North Kingstown, Rhode Island, and they have a three-year-old baby. Her father is a casualty doctor.
In her high school year book she wrote that her ambitions were to go to college and join the Peace Corps. Neighbours said she had adopted Islamic dress a few years ago after studying at Suffolk University in Boston.
Tom Menino, the Boston mayor, said Dzhokhar may have been “brainwashed or manipulated” by his elder brother.
Worshippers at a mosque in Cambridge Massachusetts described how Tamerlan stood up and began shouting at the imam during a prayer service three months ago.
The imam had mention Martin Luther King Jr and Tamerlan shouted: “You cannot mention this guy because he’s not a Muslim.” One worshipper said he was “crazy” and had “an anger inside”.