Transit SWAT officers arrived at the scene after Tsarnaev, who had also been wounded in the earlier gun battle, had already fired on other cops.
An FBI negotiator had convinced the accused bomber to surrender, but Thompson and other team members said they weren't sure he would do it.
"We had no idea if the boat was rigged with explosives," Patrolman Jeff Campbell said at a press conference Monday evening. "He could have done anything."
When they began moving in, they could see their target lying on his side in the boat, one leg and one arm hanging out of it, possibly unconscious.
They were about 10 to 15 yards away when Tsarnaev suddenly sat straight up.
"You don't really have time to be afraid," Sgt. Sean Reynolds recalled.
"At a time like that, training kicks in," Thompson added. "We don't have emotion going into something like that."
Thankfully, the suspect put both his hands up, and when the cops saw they were empty, they ran to him.
"We pulled him down and put the cuffs on him," said Thompson, the arresting officer of record in an operation that involved hundreds of cops over the course of the day.
Authorities say Tsarnaev had wounds to his head, neck, legs and hand.