Jonathan "The Duke" Mardukas (Grodin) is an accountant who embezzled $15 million from Las Vegas gangster Jimmy Serrano (Dennis Farina) and skipped bail. He is hiding in New York when his Los Angeles bail bondsman, Eddie Moscone (Joe Pantoliano), hires bounty hunter Jack Walsh (De Niro) to bring the accountant in. To get the $100,000 bounty, Jack needs to get "The Duke" back to L.A. before midnight on Friday, or Eddie forfeits the $450,000 bail and faces bankruptcy.
The FBI, led by Special Agent Alonzo Mosely (Yaphet Kotto), wants Mardukas under arrest to build their case against Serrano. Alonzo warns Jack not to interfere with his plans, but Jack, under the pretense of accepting, pays no attention, and instead pinches Mosely's identification. Serrano, meanwhile, suspects that Mardukas has access to financial information that could lead to his conviction. Additionally, that information would implicate Serrano and his ties to other mobsters, which could jeopardize his life if exposed. As a result, Serrano intends to have Mardukas killed before he can testify against him in open court.
After apprehending Mardukas in Manhattan, Jack is unable to take him to L.A. by plane due to Mardukas' professed fear of flying, which gets them thrown off their transcontinental flight. The pair embark on a wild cross-country chase (with Mardukas even temporarily piloting a plane, proving that his fear of flying was a ruse), relying on various unreliable modes of transportation, all the while dodging the FBI and Serrano's henchmen Tony (Richard Foronjy) and Joey (Robert Miranda). Moscone also hires rival bounty hunter Marvin Dorfler (John Ashton) as insurance in case Jack is unable to deliver Mardukas, but offers him $25,000, claiming he offered the same to Walsh.
Throughout their journey, Walsh and The Duke bicker constantly, due to the clash of Walsh's rough-hewn personality and Mardukas' habit of nagging. Much of the movie involves Mardukas' sincere effort to uncover the truth about his captor, a person he suspects is actually a decent man beneath his cynical and embittered exterior. He eventually learns that Jack was a former Chicago undercover detective who refused to go on the take of a heroin dealer he was building a case against. He was then drummed out of the force after being framed for heroin possession by corrupt colleagues and driven out of Chicago, his marriage ended and he became estranged from his family. His ex-wife ended up remarrying one of his colleagues, now a captain, whom Jack insinuates was one of the corrupt members of the force. Jack has not seen his daughter since she was a little girl, and has since then lost all faith in the law, explaining his profession as a bounty hunter. As the plot unfolds, it turns out that the heroin dealer responsible for Jack's framing was Jimmy Serrano himself. Jack, for his part, wants to see the job done so he can retire and open a coffee shop with his promised $100,000 bounty, aware that in doing so, he will most likely be helping Serrano avoid prison. He also has a keen sense of propriety and refuses a bribe from Mardukas, as well as a large cash offering from Serrano's camp in exchange for turning Mardukas over to them.
After making it as far as Arizona, the two are chased by dozens of police cars. They narrowly dodge the police, but Mardukas is captured by Dorfler. Finally figuring out that Moscone cheated him and how much The Duke is actually worth, Dorfler decides to give him up to Tony and Joey for $1 million. However, Dorfler inadvertently reveals where he is keeping the fugitive, and is knocked unconscious. Mardukas is captured by Serrano's men, and Dorfler, defeated, decides to go home.
Walsh, meanwhile, is finally found by Mosely and his men, and taken into custody. An enraged Walsh calls Moscone and furiously berates him for hiring Dorfler as insurance. Moscone, however, reveals that Dorfler is not delivering The Duke to him, and Walsh realizes that Dorfler has delivered Mardukas to Serrano. Walsh calls Serrano's men and tells them that Mardukas gave him computer disks with enough information to put Serrano away (earlier, Mardukas had informed Walsh that he intended to backup files on to disks but never did). Walsh threatens to turn the disks over to the FBI unless Serrano himself returns The Duke to him at McCarran International Airport in Las Vegas. Walsh tells Mosely and the FBI of his plan to deliver Serrano to them (even though the disks to be used in the sting are blank, Serrano's taking possession of them would be enough to indict him for conspiring to destroy government evidence and obstruction of justice), but will only carry it out if he is allowed to return Mardukas to Moscone personally and collect his money. Mosely, since his primary target is Serrano, accepts Walsh's proposal.
At the airport, Serrano and Walsh confront each other for the first time since Jack left Chicago. The exchange is interrupted by Dorfler, who sees the exchange going on, not knowing that the FBI are watching and waiting for Serrano to take possession of the disks. Jack, whose microphone wire gets knocked out by Dorfler, yells to the FBI that Serrano has the disks. The FBI move in, arresting Serrano, his men, and Dorfler.
As bargained with Mosely, Jack takes the Duke back to Los Angeles. He calls Eddie Moscone and tells him he has Mardukas in L.A. before the deadline - but he is letting him go. Before Jack can leave, they exchange gifts - Jack hands The Duke his broken watch, and Mardukas hands Jack a money belt he had hidden on his person throughout the film, filled with $300,000 in $1,000 bills: he was planning on leaving before Jack showed up, so he didn't have time to use the money. The two part as friends. Mardukas then disappears, and Jack tries to get a cab. However, since the driver doesn't have change for a thousand dollar bill, he zips up his leather jacket and pulls up his collar, preparing to walk home.