Not that it's any easier when the Alabama is first taken over. Phillips sends much of his crew to hide within the vast bowels of his ship as he and a few colleagues deal with the boarding party as best they can.
The movie's snowballing anxiety levels aren't just a product of Indian Ocean swell combining with Greengrass' sharply-edited shakycam. The performances of Tom Hanks as Phillips and Barkhad Abdi as Muse, the leader of the Somali pirates, create their own electricity.
From the moment Muse declares "I am the captain now" as he holds an AK-47 to Phillips' head on the Alabama's bridge, it's clear there will be a battle of wills between the two and any Stockholm Syndrome is a long way off.
Greengrass might be at sea but actually he's on familiar ground. The former journalist has already brought his documentary sensibilities to bear on Northern Ireland's troubles in Bloody Sunday and United 93, which told of the one airliner in the 9/11 hijackings that didn't make its target.
And like United 93, this - despite being based on Phillips' autobiographical account A Captain's Duty: Somali Pirates, Navy SEALs, and Dangerous Days at Sea - takes a wider view.
It starts with Phillips' preparation for the voyage from Oman to Mombassa, flying in from his comfortable New England home and family.
It also takes us ashore in Somalia where the local warlord orders Muse and his mates to sea as pirates on the international trade route skirting their coastline, clambering aboard the slow-moving and unarmed ships and waiting for a payday.
The way the movie draws them. you can't help but admire the foolhardy commitment of these skinny men pursuing their great white whale in outboard-powered skiffs, the giant ship attempting to spout them away with its firehoses and lumbering evasive manoeuvres.
At times this movie can feel like a nautical Zero Dark Thirty, especially with its depiction of the US Navy rescue mission drawn as an exercise in all-American ruthless efficiency. But, it's not a film about anti-US terrorism.
"This is business," Muse reminds Phillips, during his ransom demands. Later he tells him he's just doing what he's been ordered by his bosses.
"We all have bosses," replies a weary Phillips.
But the stoic Phillips and the skittery Muse and his volatile cohorts are, of course, worlds apart. And while Greengrass and scriptwriter Billy Ray want to explain the whys of Somali piracy and the desperate men behind it, this movie is really about Phillips' survival.
If, at the beginning, Hanks seems suitably cast as yet another ordinary guy thrown into extraordinary circumstances, by the end, it's become an emotionally riveting performance. His Captain Phillips makes Captain Phillips a true-life story that actually rings true.
Cast: Tom Hanks, Barkhad Abdi
Director: Paul Greengrass
Rating: M (violence)
Running time: 134 mins
Verdict: A 21st century pirate movie with a gripping performance from Hanks.
Stars: 4/5
