In both the movie and in the real thing, Captain Phillips and his crew prevented the pirates from taking over the ship.
Instead, they took $30,000 from the ship's safe and headed for Somalia in a lifeboat. Hard to believe, but Phillips considered that something of a victory.
"Most of my problems were solved once I got into that lifeboat," Phillips told Martin.
"My crew was free and clear, my ship was free and clear, the cargo was free and clear. . . All I had to worry about was myself. All I had to worry about was one person."
Even though Navy warships were shadowing them, Phillips was at the mercy of trigger-happy pirates.
"In the movie you sort of feel a change from a hostage standoff to, 'One of us isn't getting out of here alive.' Did that happen aboard the lifeboat?" asked Martin.
"That actually happened," Phillips said. "They would tell me I would die in Somalia, and they would die in the United States."
"How close did you come to dying?"
"I was close enough during the whole time," Phillips replied. "At any point, you know, a slipped finger or maybe instead of pulling and firing on an empty chamber, maybe it was full. The young pirate with the wild Charlie Manson eyes, he loved having that rifle there, pulling the trigger and smiling at me."
"Were you afraid?"
"I was afraid during the whole time, yes," he said.
WEB EXTRA:from Richard Phillips' account, "A Captain's Duty: Somali Pirates, Navy Seals, and Dangerous Days at Sea" (Hyperion Books).
But then Phillips took the extreme measure of trying to escape. Other than compressing five days into two hours, the movie -- including its depiction of the captain's attempted escape -- stays remarkably faithful to the facts.
Once back in the lifeboat, Phillips was tied up very tightly. "I've still got numbness and scars today," he said. "The leader was very upset at his three men, and he was screaming at them, they were screaming at me, hitting, flailing me."
Phillips and the pirates didn't know it, but Navy SEALs had parachuted into the Indian Ocean and now had the lifeboat in their sights.
"When the shooting started, I heard a noise, and I got sprayed with debris in my face, and I just dove down into my seat," Phillips said.
The Maersk Alabama's captain had been rescued. What happened next is probably the most powerful scene in the movie. The studio won't let us show it, but it features another unlikely star, Navy Hospital Corpsman Danielle Albert.
"My first take was terrible!" she laughed.
She had auditioned for a bit part, ("I was not going to let somebody else be the doc on this ship!") and suddenly ended up opposite one of the biggest movie stars in America, which she found "very intimidating!" The scene was shot in the sick bay of a Navy destroyer.
"Tom Hanks came around the corner and I froze," HM Albert said. "I didn't know what to do. It was terrible and I broke out in hives, and it was bad!"
Martin asked, "What did it take to get you over your stage fright?"
"I was in tears, and I didn't know what I was doing, and so Tom, he was sitting here, and he got off the bed and he's like, 'Doc, do you need to sit down? Do you need some medical attention?' " and I'm like, 'Yeah!' "
"We did it again and I did it exactly, exactly what I would do in a real situation," she said.
"It ended up being an extraordinary thing," said Hanks, "because movies are fake things, but that was a real scene that we shot, you know, because it was not rehearsed, it wasn't planned, it wasn't written."
But the most realistic depiction of all belongs to Barkhad Abdi, as the pirate captain who set out to hijack an unarmed container ship and ended up taking on the U.S. Navy.
"Barkhad really did it," said Phillips. "In his eyes you really saw, and his acting, that, that he was very close to the real thing."
Remember that this winter when the Oscar for Best Supporting Actor is handed out.
CBSNews.com's complete movie coverage
For more info:
- "Captain Phillips" (Official site)
- "A Captain's Duty: Somali Pirates, Navy Seals, and Dangerous Days at Sea" By Richard Phillips with Stephen Talty (Hyperion)