It was specialized training that allowed them to act so quickly, Clark County Sheriff Joseph Lombardo told CBS' 60 Minutes.
"I think they prevented a thousand deaths, and I think it's important for the American public to understand that," Lombardo said.
Lombardo had traveled to Mumbai, India, after the November 2008
terrorist attacks on hotels and other sites that left 164 people dead. The sheriff gleaned insight from the trip, he said, and the department now reacts more quickly to such shootings, forming a team to "cease the action'' of the assailant.
"Before we were trained to form a perimeter and hope for the best," Lombardo said. "Now we're trained to gather up and go get it."
Racing to the Mandalay Bay
Detective Matthew Donaldson was doing paperwork when radio calls went out reporting an active shooter. He jumped in a car and drove 9 miles to the Mandalay Bay Hotel and Casino, he said in the "60 Minutes" interview.
Donaldson ran the last few blocks to the hotel, he said, but he ditched the cowboy boots he was wearing in the casino because they hurt his feet.
"I was faster barefoot and I was going to be more effective barefoot," he said.
Not far away, K-9 officers Dave Newton and Sgt. Joshua Bitsko were training dogs when they heard the radio call.
"I just yelled to these guys, 'Let's go. There is an active shooter,'" Bitsko recalled saying.
The pair drove to the scene. At the hotel, they met up with Levi Hancock, a SWAT officer who was armed with explosives, and zeroed in on the 32nd floor, where other officers had pinpointed the shooting. Bitsko thought there might have been more than one gunman.
By that time, Paddock had shot through the door at Jesus Campos, a Mandalay Bay security officer who had gone to respond to an alarm, striking him in the leg. Police said that Paddock stopped firing on the crowd after Campos approached his door.
'Hurry but be quiet'
The four-man team found the stairwell door to Paddock's hallway barricaded.
"He had screwed shut the door with a piece of metal and some screws in the stairwell going out to the hallway right by his door," Bitsko recalled.
The SWAT officer used a pry bar to pop the door open, Newton said.
Down the hall, the door to Paddock's room was riddled with bullet holes.
"It looked like Swiss cheese," Newton said.
The SWAT team member quietly set explosives to blow open the door, hoping not to arouse the shooter's suspicions, said Newton.
"Hurry, hurry -- hurry but be quiet," Newton remembered saying.
They didn't know where Paddock was in the room. It was just over an hour after the last shots had been fired. Bitsko said it was like a "deadly game of hide and seek."
"I remember thinking, 'Man, I wish I had my dog with me because it's nice to have him lead the team,'" Bitsko said.
"Breach. Breach. Breach," someone said on the police radio.
The explosion set off alarms. The door was open, and the group swarmed the room.
Inside, the officers found drills and other tools, along with drill bits, phones, laptops, guns and ammunition. They also discovered Paddock's body.
'Tripping over guns'
The room smelled like gunpowder, Bitsko recalled.
"We were tripping over guns," he said.
Authorities recovered 23 guns from Paddock's room, police said.
Officers also found a handwritten note with calculations of distance and trajectory from his window to the crowd below, Newton said.
Authorities have received more than 1,000 tips, but are still struggling to determine what motivated Paddock, who didn't have a criminal record, to carry out the attack.
"He had tool boxes and power tools to run wires for his surveillance system. Everything that he had, it took him days to finish," Bitsko said.
'Blood dripping on my hand'
The FBI searched Paddock's Mesquite, Nevada, home early Sunday, Mesquite Police Chief Troy Tanner told CNN. In the evening, the lights along the famed Las Vegas Strip dimmed for 11 minutes to honor the victims and heroes of the attack at the Route 91 Harvest Festival, which left 58 people dead and injured nearly 500.
Las Vegas Detective Casey Clarkson was not part of the team that breached the hotel room, but he was among those injured in the shooting, he told "60 Minutes."
Crouched below on the street, Clarkson recalled the bullets were like white sparks, "like powder almost ... hitting the concrete, hitting the van." Clarkson was grazed in the neck.
The rounds rained down next to the officers at street level. Clarkson wondered how the shooter could be so accurate, he said. He remembered becoming lightheaded.
"It was already ... blood dripping off my hand," he said.
But he wanted to help as many people as possible, he said. So he stayed.
This story has been updated to reflect the latest timeline of the shooting and response put out by police.