Teresa "Terry" Doolittle (Whoopi Goldberg) transfers funds for the First National Bank in Manhattan, New York. She does not quite fit with the bank's corporate image, despite being a good employee and popular with her co-workers. However, she is often chastised by her no-nonsense boss James Page (Peter Michael Goetz).
Set against the backdrop of the pre-Glasnost Cold War, Terry is contacted over her AC computer desktop by an unseen man calling himself "Jumpin' Jack Flash" who turns out to be a British Intelligence agent in Eastern Europe that is being pursued by the KGB. After being given a riddle for his password, Terry determines the password to be B-flat, after the key in which "Jumpin' Jack Flash" is supposedly written (as the actual song by The Rolling Stones is recorded in the key of B-flat). Jack sends her to the British Consulate to deliver the message "Dog's barking, can't fly without umbrella" to Department C. Despite feeling ludicrous, Terry delivers the message to the head consulate Jeremy Talbot (John Wood) who is apparently puzzled and sends Terry away, telling her there is no Department C. Jack then asks her to enter his apartment in New York to retrieve a frying pan, on which are Jack's CIA contacts to acquire a passport.
Shortly after her visit to the British Consulate, Terry begins to be monitored. Peter Caen (Stephen Collins), a CIA agent working under the alias Marty Phillips, arrives at First National Bank as a new co-worker of Terry in order to spy on her.
One evening, after Jack tells Terry to retrieve the frying pan from his apartment, a computer technician (James Belushi) shows up to repair her terminal, but when Terry calls Sperry Corporation to confirm his identity, the technician vanishes. After Terry aquires the frying pan from Jack's apartment, the computer tech appears again as a taxi driver, who tries abduct her, but Terry bashes him on the head with the frying pan and escapes.
Another day later, Terry is finally contacted by one of Jack's contacts, Mark Van Meter (Jeroen Krabbé), who meets her at the docks. After being stunned to realize Terry is a banker and has no relationship at all with the intelligence community, Van Meter notices they are being watched and pushes Terry off the docks and into the East River to save her life, but is shot and killed himself by unseen assasins. The police dismiss Terry's claim of the murder and Peter bails her out of jail.
Unsure who to trust, Terry contacts Jack on the computer again who then tells her how to break into the British Consulate central computer. Conning her way in under the guise of an entertainer, she manages to enter the mainframe, but Talbot deactivates the computer link before Jack receives a contact. Going through one of Jack's romantic contacts, Lady Sarah Billings (Sara Botsford), Terry is rebuffed and then captured by the KGB, who lock her in a phone booth and drag her around the city. After escaping when the booth is knocked over, Terry is injected with truth serum by the computer tech (now posing as a police officer), but escapes after trapping his arm in a car window and rolling the car into traffic.
Terry again contacts Sarah and makes an impassioned plea for her help. Sarah tells Terry she would rather let Jack be killed than risk losing face. A disgusted Terry chastises Sarah for her indifference to Jack's plight and walks out. She then stumbles into work and after embarrassing Mr. Page by yanking off his fake hairpiece in front of the entire office, passes out.
Terry awakes at home and is dropped in on by Sarah who has had a change of heart and gives her a contact so Jack can use to escape. After passing the contact to Jack, she is again captured by the KGB and learns that the contact is a KGB mole who turns out to be Talbot himself. After nearly being tortured with a power sander, Terry escapes and is caught by police. After realizing the police are arresting her rather than protecting her, Terry escapes. She rushes to the bank and is again ambushed by the KGB and Talbot. After struggling with the KGB and biting Talbot's groin, she confirms to Jack that the contact will kill him. Marty identifies himself as Peter Caen and gives Jack the correct contact.
At the end, after initially not showing up at a restaurant where he and Terry plan to meet, Jack (Jonathan Pryce) appears in her office to thank her personally by taking her out to dinner.