As George Stroud, editor-in-chief of Crimeways magazine, hides from security guards in the clock tower of the Janoth Publications building in New York City, he reflects on the fact that thirty-six hours before, he was leading a normal life as a Janoth employee: George, who is finally about to go on his honeymoon after seven years of marriage, is ordered by his tyrannical boss, Earl Janoth, to go on assignment or be fired.

Fed up with being loyal to a firm that is jeopardizing his family life, George quits.  He then joins Janoth's mistress, Pauline York, in a bar and misses his honeymoon train while drowning his sorrows.  Pauline, also tired of Janoth's egocentric manipulations, offers to help George humiliate Janoth by writing a torrid biography of him.  After George tells Pauline that Janoth fired a man earlier in the day for choosing red ink over Janoth's preferred green, they go on a drunken search for a green clock as a "present" for Janoth, who is obsessed with time.

While in an antique shop, George and Pauline out-bid a middle-aged woman for a Patterson painting, unaware that she is the eccentric Louise Patterson herself.  Later, they visit Burt's Sports Bar, which George frequents, and George introduces Pauline to McKinley, a radio actor friend whose roles have included President McKinley and Jefferson Randolph.  Playfully fulfilling their quest for a green clock, Burt gives George and Pauline a sundial, then adorns it with a green ribbon.  Eventually, George takes Pauline home and collapses in a drunken stupor on her couch.

Around one-thirty in the morning, Pauline sees Janoth arriving and rushes George out the door with his painting.  Before reaching Pauline's door, Janoth catches a glimpse of a man catching the elevator, and he and Pauline then quarrel about their respective infidelities.  Pauline tells Janoth she spent the evening with a man named Jefferson Randolph.  When Janoth insults her, Pauline cruelly declares that women only go out with him for his power and position.  Enraged, he stabs her with the sundial, killing her.  He then calls one of his loyal editors, Steve Hagen, for help, and Hagen goes to Pauline's apartment and sets her clock back.  He also takes George's handkerchief that was soaked in green liquor from Pauline's purse, and returns the sundial to Burt's bar.

George, meanwhile, has flown to Virginia to meet his wife Georgette, and tells her that after he missed their train, he walked the streets despondently because she had not waited for him.  Janoth telephones and apologizes before asking George to locate a man named Jefferson Randolph.  George believes Janoth is trying to find the man who was seen with Pauline and feels compelled to return to New York.  There, George sends his staff out on assignment to locate Jefferson Randolph, then tries to hide the fact that the descriptons all point to him.  One staff member, Don Klausmeyer, figures out that the blonde seen with Jefferson Randolph the previous night is a model named Pauline York and goes to her apartment.

George arrives first and finds Pauline dead, turns the clock ahead, then goes to confront Janoth about why he did not go to the police.  Janoth craftily says he merely wanted the exclusive on a good story.  As witnesses to Pauline and George's drunken antics are gathered in the Janoth building, the antiques dealer spots George in the lobby and tells Janoth that the killer is in the building.  George is now trapped, unable to interview a cabbie who took Janoth home following the murder.

Hagen, meanwhile, has printed an article in the evening newspapers offering a reward for a missing Patterson painting, hoping to bait the killer.  Georgette, finding the painting in her bedroom, goes to George's office to confront him about his affair with Pauline York.  After he explains everything to her, she agrees to locate the cabbie.

Then Louise Patterson arrives to sketch a picture of the man who bought her painting.  As soon as she realizes that he is none other than George, she offers to protect him in exchange for money.  Janoth, meanwhile, has ordered his bodyguard, Bill Womack, to pay the cabbie to skip town, and Georgette ends up back at the building.  At the same time, several witnesses are touring the building in search of Jefferson Randolph.

While George and Georgette hide in Hagen's office, she finds George's handkerchief in Hagen's cigarette box, and George decides to try and frame Hagen for the murder in order to draw out Janoth.  George then goes into the clockworks and, having mulled over the last thirty-six hours, takes action.  George calls the cab company and learns that Hagen took a cab from Pauline's apartment early that morning.  After George mistakenly hits a switch that momentarily stops all the building's clocks, Janoth sends an armed Womack to catch the man in the clock.  George traps Womack in a stalled elevator and escapes into Hagen's office, where Georgette has brought McKinley.  George then tells Janoth and Hagen that he has found the killer, and when they arrive, he introduces McKinley as a police inspector, and accuses Hagen.  Although Hagen calls George's bluff by recognizing McKinley as a regular at Burt's bar, McKinley says he saw Hagen return the murder weapon.  After Janoth assures Hagen that he will provide Hagen with the best legal counsel, Hagen blurts out that Janoth killed Pauline.  Janoth shoots Hagen and runs out.  Although George tries to warn him not to take the elevator, Janoth fires a poorly aimed bullet at George before falling to his death in the elevator shaft.  Louise then discovers McKinley, her long-lost fourth husband, and George calls the police as Georgette kisses him.