"Sailor Costigan and the Turkish Menace" revolves around Steve Costigan's unexpected adventures in Shanghai. The story begins with Steve wandering the city's waterfront, feeling restless and eager for the arrival of his ship, the Sea Girl. His primary concern is reuniting with his beloved bulldog, Mike, whom he left on the ship.

As he walks, Steve witnesses a young man being attacked and robbed of his briefcase. Acting on instinct, Steve chases the assailant through dark, winding alleys but eventually loses him after a clumsy fall. Unbeknownst to Steve, the victim of the assault is Goslin, the paymaster of the Anglo-Oriental Company, who was carrying a significant payroll amount.

Steve, mistaken by Goslin as the attacker due to a brief glimpse during the chase, becomes a prime suspect. Goslin, having only seen Steve's silhouette, describes him to the police as a large, black-haired sailor with cauliflower ears—a description that unfortunately fits Steve all too well.

To avoid police detection, Steve decides to lay low. However, his friends Mike Dorgan and Bill McGlory, who are engrossed in their own debate about wrestling abilities, inadvertently involve Steve in further trouble. Bill is intent on wrestling Abdullah the Terrible Turk at Kalissky's Arena, despite warnings about Abdullah's prowess.

At the wrestling match, the situation escalates. Bill uses a unique wrestling technique against Abdullah, but the match turns into chaos when the police raid the arena, having followed Steve there. In the ensuing melee, Steve, Bill, and Mike end up fighting not only Abdullah but also several other men who were conspiring with the Turk.

During the fight, a briefcase similar to the one stolen from Goslin surfaces, leading to a series of misunderstandings and accusations among the characters. Eventually, it's revealed that Abdullah himself was the actual thief. The story concludes with the police arresting Abdullah and clearing Steve, Bill, and Mike of all charges related to the payroll theft, thanks to the evidence and circumstances clarified during the brawl.