The man then took their 2011 Nissan Rogue, they said.
It was not clear how long he had been there, a bag of carrots and milk were in the refrigerator, they said.
At around 12:20 p.m., some 15 minutes after he left, they freed themselves and called 911 to report the incident, they said.
"We're very happy to be alive," Karen Reynolds said. "I didn't wish him dead though ... I prayed for him a lot and I'm praying for his family now."
A 'guy with a big gun'
At 12:45 p.m., Fish and Wildlife wardens spotted the SUV and began pursuing it.
The wardens, driving in separate vehicles, chased Dorner, and a gunbattle ensued. One of the warden's cars was hit, and Dorner crashed his car and ran, according to authorities. He then carjacked a pickup truck.
Rick Heltebrake, a camp ranger, said he was driving when he saw the crashed purple vehicle -- and then something terrifying.
"Here comes this guy with a big gun, and I knew who it was right away," Heltebrake told CNN affiliate KTLA. "He just came out of the snow at me with his gun at my head. He said, 'I don't want to hurt you. Just get out of the car and start walking.' "
Heltebrake said the man let him take his dog and walk away with his hands up.
"Not more than 10 seconds later, I heard a loud round of gunfire," Heltebrake said. "Ten to 20 rounds, maybe. I found out later what that was all about."
Dorner fled to a nearby cabin and got into another shootout, this time with the San Bernardino County deputies, killing one and wounded another.
Some of the firefight between police and the suspect was captured live on the telephone of a reporter for CNN affiliates KCBS and KCAL. Police in Los Angeles listened live over police scanners broadcast on the Internet, LAPD Lt. Andy Neiman said.
"It was horrifying to listen to that firefight," he said. "To hear those words, 'officer down,' is the most gut-wrenching experience you can have as a police officer, because you know what that means."
Audio from a Los Angeles television station captured the sound of someone early in the standoff shouting, "Burn it down ... burn that goddamn house down. Burn it down." It's not clear who used those words.
But the order to use smoke canisters -- "burners" -- didn't come for another two hours, according to San Bernardino County sheriff's radio traffic.
"Seven burners deployed, and we have a fire," one officer reported at 4:16 p.m. (7:16 p.m. ET).
Five minutes later, a single gunshot was reported from inside the house. A senior officer ordered units around the cabin, "Stand by. Maintain your discipline." About a minute after that, officers reported ammunition exploding inside.
Sheriff's investigators confirmed overnight that they had found charred human remains among the ashes.
Dorner cheered in some quarters
Dorner had vowed to kill police officers to avenge what he called his unfair termination. He was fired after accusing his training officer of kicking a suspect during a July 2007 arrest, a complaint the LAPD concluded was unfounded.
The department accused him of lying to superiors and to internal affairs investigators and forced him out in January 2009. Dorner challenged his dismissal in court but was unsuccessful.
Dorner was first named a suspect in two shooting deaths on February 3: Monica Quan, the daughter of his police union representative, and her fiance, Keith Lawrence.
Police say he killed Crain and wounded Crain's partner in an ambush on their patrol car February 7. They say he also wounded an LAPD officer who chased him in the suburban city of Corona, California.
In a manifesto announcing his planned rampage, Dorner said nothing had changed in the LAPD since its scandals of the 1990s, the Rodney King beating and the Rampart police corruption case. Those allegations have struck a chord with some who say that, despite the four killings, Dorner was seeking justice.
Shadowed by that history, LAPD Chief Charlie Beck announced Saturday that the department would re-examine its proceedings against Dorner. The review is "not to appease a murderer," but "to reassure the public that their police department is transparent and fair in all things we do," he said.