Convenience store robber Herbert I. “Hi” McDunnough and police officer Edwina “Ed” meet after she takes the mugshots of the recidivist. During subsequent visits, Hi learns that Ed’s fiancé has left her. Hi proposes to her after his latest release from prison, and the two get married. They move into a desert mobile home, and Hi gets a job in a machine shop. They want to have children but Ed is infertile, and they cannot adopt because of Hi’s criminal record, even though Ed is a police officer. Devastated, Ed quits her job. The couple learns of the “Arizona Quints,” quintuplet sons of locally famous furniture magnate Nathan Arizona; driven by envy, Hi and Ed kidnap one of the babies, whom they believe to be Nathan Junior. Hi and Ed return home and are soon visited by Hi’s cellmates, Gale and Evelle Snoats, who have just escaped from prison. Facing ridicule by the Snoats brothers for his new domestic life, Hi is tempted to return to his felonious ways. That evening, Hi has an intense nightmare in which he foresees the arrival of an apocalyptic biker, later revealed to be bounty hunter Leonard Smalls.
The next day, Hi and Ed are visited by Hi’s foreman Glen and his family. Glen’s wife Dot speaks of her desire to have more children with Glen, while Glen confesses to Hi that he and Dot are swingers, and he proposes exchanging wives. Hi assaults Glen in his wrath and chases him off the property. That night, Hi robs a convenience store and steals a package of diapers for Junior, but Ed, furious, ditches him, forcing Hi to escape on foot from the police, two armed cashiers, and a pack of dogs. Glen returns the next day to fire Hi, and reveals that he has inferred Junior’s identity because of the newspaper article he read about Junior missing. He threatens to turn Hi in to the police unless Glen and Dot get custody of Junior. Gale and Evelle overhear this conversation and overpower Hi in a wild fight in his home, tying him to a chair and taking Junior for themselves. When Ed comes home, she frees Hi and the two arm themselves and set out together to retrieve the child. Meanwhile, the bounty hunter Leonard Smalls approaches Nathan Arizona Sr. with an offer to find the child for $50,000. Nathan Sr. declines the offer, believing that Smalls himself is the kidnapper. Smalls decides to recover the child anyway to sell on the black market.
Gale and Evelle rob a bank but leave Junior there as they make their getaway. One of the bank’s anti-theft dye canisters explodes in their loot sack, blocking the car’s windows and incapacitating them. At the bank, Smalls arrives for Junior just ahead of Ed and Hi. Ed grabs the baby and flees; Hi is able to fend Smalls off for a while, but is eventually overwhelmed by Smalls’s superior strength, armament and viciousness. As Smalls throws Hi to the ground and prepares to kill him, Hi holds up his hand to reveal that he has pulled the pin from one of the hand grenades on Smalls’s vest. Smalls cannot get rid of the grenade in time and is blown to pieces when it explodes and sets off all his weapons. Hi and Ed sneak Junior back into the Arizona home and are confronted by Nathan Sr. After Nathan Sr. learns why they took his son, he sympathizes with their predicament and decides not to turn them in. When Hi and Ed say that they are splitting up, he advises them to sleep on it. Hi and Ed go to sleep in the same bed, and Hi has a dream about Gale and Evelle returning to prison, realizing they “weren’t ready yet to come out into the world”; Glen gets his due from a Polish-American police officer whom he has no luck getting to listen to his “wild tales” about Hi and Ed after he “threw in one Polack joke too many”; and Nathan Jr. gets a football for Christmas from “a kindly couple who wish to remain unknown”, later becoming a football star. The dream ends with an elderly couple (implied to be Hi and Ed) together enjoying a holiday visit from a large family of children and grandchildren.