Eugenijus Tulauskas, from Lithuania, was up to four times over the maritime limit when arrested in September last year.
A pilot had to take control of the container ship to ensure its safe passage into harbour.
The 44-year-old seaman, of no fixed abode was fined Â£1,500 at Belfast Magistrates' Court.
Tulauskas had contested a charge of having excess alcohol while on duty as professional master of a ship.
His lawyers argued that he was not on duty at the time of the offence.
The court was told that an experienced pilot sent out to guide the ship into port thought he smelled alcohol on Tulauskas' breath.
He contacted Belfast Harbour Police who detained the defendant and took a breath sample.
Talauskas confirmed at that stage he had not taken any alcohol in the previous four hours.
The district judge said she was "satisfied on the evidence that the defendant was not just master of the vessel, but was on duty at the time".
Talauskas' lawyer argued that he was aware of the pilot's actions and had congratulated him on his manoeuvres.
"It's not a case that he was totally incoherent," the lawyer said.
The court heard that the captain had since lost his job.
The judge, who could have fined him up to Â£5,000, commented that "if the defendant were in employment I would be looking at the upper region (of a fine)".

The raiders targeted the Central England Co-operative property on Chesterfield Road in Duckmanton at about 04:00 BST.
The owner of nearby business WB Motors, Ian Womack, said the raiders had torn down the front of the shop.
Mr Womack said: "It looks like they devastated the property to be fair - the whole front has fallen down."
He said: "There's a large piece of machinery - a JCB - was taken from a building site around the corner - and half the shop front has been pulled down by the JCB to take out the cash machine.
"It will be weeks before it is sorted out. It was not just the cash machine that was stolen - the whole front wall was pulled out."
Mr Womack said the Co-op was cordoned off by police when he arrived at work, adding that CCTV images from his forecourt "would probably identify the culprits".
He said an abandoned vehicle found nearby would also provide "some interesting evidence".
A Co-op spokesman said: "While the building is structurally sound, at present we cannot say when we will be able to open the store again for trading."
The culprits fled the scene in a white Vauxhall van and police are appealing for witnesses to contact them.
The cash machine and van were found later by officers near Buttermilk Lane, police said.
A police spokesman said several vehicles were involved, but officers were "still trying to piece together exactly what happened".

Four steel columns need to be installed at Scarthin Books, in Cromford, Derbyshire, to support the weight of about 100,000 books over four floors.
A crowd funding appeal began on Sunday and more than £5,000 has been raised.
Manager David Booker said building work was put off in favour of restocking during the shop's 41 years.
The shop, which has four floors and a vegetarian cafe, was dubbed one of the best in the world by The Guardian, in 2008.
It was also used as a set for the film When Did You Last See Your Father, in 2007.
However, a number of cracks have appeared on the walls and the staircases between floors are bowing.
Mr Booker said customers have often questioned how the bookshop "has stayed upright" and after a survey by a structural engineer, fears were realised.
"He said we needed to do some fairly sharpish structural work," said Mr Booker.
"It's a bill we could do without as an independent bookshop with tight financial constraints."
He said despite the costs of its upkeep moving out of the building had never been a consideration.
"The building itself is more than half of the overall character of Scarthin itself... people travel from far and wide.
"It's our priority to make sure this place stays standing for another 40 years."
The appeal has raised £5,510 in three days by the shop's customers who will receive a number of rewards in return.
A sea captain has been convicted of being drunk in charge of a merchant ship in Belfast Lough.
[NEXT_CONCEPT]
Thieves used a JCB to smash into the front of a filling station store during a cash machine raid in Derbyshire.
[NEXT_CONCEPT]
A bookshop once named as one of the best in the world could fall down unless £10,000 can be raised for structural repairs, say its owners.