Tintin and Snowy are walking around one day when Snowy starts digging in a garbage can, finds a can with a crab painted on it inside and digs it out. Tintin scolds Snowy for this, since the can could have cut him, and throws it away. They meet up at a cafe with Thomson and Thompson, who are investigating a case of counterfeit coins. When Tintin follows them back to their office, he notices that they have half a picture of a crab on their table. According to Thomson and Thompson, it came from police headquarters--from a man who drowned at sea and had five counterfeit coins in his pocket.
Tintin rushes out to find the picture, and Thomson & Thompson follow him. They rummage through some garbage cans but are unsuccessful; the garbage man tells a random Asian man notices they are searching for a crab tin and the Asian remarks to himself, "A crab tin! Are they indeed!"
Tintin takes the crab picture back to his house. He tries to examine it with a magnifying glass but initially confuses the glass with Snowy's bone. When he does manage to examine, the picture, it reads: Karaboudjan. Tintin thinks it's an Armenian name. Later, Tintin's landlady is attacked, and she says an Asian man tried to reach Tintin earlier and give him a letter before being kidnapped by some gangsters.
Thomson & Thompson call, saying that the drowned body has been identified as Herbert Dawes; he was a sailor on the merchant-ship Karaboudjan. Tintin and Snowy rush to the docks to find the ship and are nearly killed by a falling crate (which Tintin manages to avoid after being distratced by seagulls). Thomson & Thompson follow Tintin up to the ship to investigate, and while they are busy Tintin is knocked out and imprisoned; Thomson & Thompson leave the ship.
The ship sails, and the gangsters receive a telegram asking to "send T to the bottom". A gangster, "Pedro", has already gone down to Tintin with food, and when Tintin asks to be untied to eat with his hands, he uses the opportunity to tie Pedro up and escape. Tintin and Snowy break into a room filled w/crates of crab tins filled w/opium and bottles of champagne. When night falls, Tintin and Snowy rope they way up to the window on the floor above them, where they run into a drunken Captain Haddock -- who professes innocence to the opium charges. Haddock suspects his first-mate, Allan, is guilty.
The gangsters come upstairs, but Tintin is hiding under the bed, while the gangsters are "shot at" by the champagne bottles downstairs. Meanwhile, Tintin, Snowy and Haddock have escaped via rowboat. While Tintin sleeps, Haddock, drunk, builds a fire in the middle of the boat to keep warm, causing a struggle between him and Tintin that sends the boat toppling over. A seaplane then appears and shoots at them. With Pedro's gun, Tintin shoots the plane down, dives under the water, appears from the surface to take the pilots by surprise and takes control of the plane.
Up in the air, the gangsters refuse to talk, and Tintin tries to steer towards Spain. Haddock, who gets drunk on another bottle of whiskey, throws a fit to seize the controls from Tintin, smashing the bottle against his head. The plane crashes into some sand dunes, but Tintin rescues the pilots from the burning wreck. The pilots then disappear, Tintin and Haddock suffer hallucinations and fall out cold before being rescued by Muslim riders in the serve of Lieutenant Delcourt, who is in command of the outpost at Afghar. He offers them some spirits, but Tintin says, "No thank you. I never drink spirits." To which Haddock adds, "Er...er..no thank you, Lieutenant, I... I don't either. I... I never touch spirits." On the radio, they hear a report that the Karaboudjan is lost at sea and may have sunken, but they are skeptical.
They leave that day with two guides, but are shot at by 20 Arab riders. Haddock rushes at them and apparently scares them away, when in fact the Lieutenant's army is the one repelling them. Several days later, they reach Bagghar, a large Moroccan port, hoping to hear news of the Karaboudjan from the harbor master. Tintin thinks he sees one of the gangsters and runs after him, accidentally losing Haddock but also losing the person he's chasing after. Haddock apparently spots the Karaboudjan disguised as the "Djebel Amilah", but gets in trouble with the police during a drunken disturbance at a cafe and is arrested. Then he's released -- only to be captured by the kidnappers, which Tintin witnesses. Tintin's attempt to chase at their car in a cab (while he scares a passenger out of the cab with the "rabid" Snowy) proves unsuccessful.
In the marketplace, Tintin runs into Thomson and Thompson, and together they spot a shop selling crab tins. These tins do, in fact, contain crab, and the merchant says he got them fro Mohammed Ben Ali, who in turn says he got them from Omar Ben Salaad, "the biggest trader in Bagghar." Tintin, dressed as a beggar, manages to locate Salaad's headquarters (Snowy sneaks in through the ventilator shaft), and they find a secret entrance in a barrel that takes them down to where Haddock is being held.
A struggle ensues, and Tintin and Haddock and Snowy barricade themselves in a wine room, where the fumes of spilled wine intoxicate them (and puts Haddock in a drunken rage that sends the gangsters running out screaming). Thomson and Thompson, meanwhile, interrogate Salaad, who is outraged when they accuse him, but the Captain appears from behind a bookcase and Salaad's secret entrance his leg and he accidentally shoots a chandelier that lands on his head, knocking him out. The police take Salaad into custody while Tintin goes on a boat chase after the escaped mate, "the most dangerous of the lot", finally managing to capture him in a fishing net.
Afterwards, Tintin is approached by Bunji Kuraki of the Yokohama police force, aka the Asian man. He apparently was imprisoned in the hold of the Karaboudjan the whole time. He tells Tintin that the dead man Herbert Dawes had alerted him to the drugs in the Karaboudjan and that Dawes, before getting whacked, had had the label with "Karaboudjan" written on it in his pocket in order to tell Kuraki the name of the ship (but he had never actually given Kuraki the paper itself).
Some days later, on the Home Service radio show, Captain Haddock is supposed to read a broadcast about "drink, the sailor's worst enemy." At the same time, Snowy receives a package containing an oversized bone ("from an admirer"). On the show, however, Haddock is "taken ill", and when Tintin calls to inquire, he is told that the Captain "was taken ill after drinking a glass of water."