Deadline at Dawn
(1946)

A sailor on leave, Alex (Bill Williams), wakes up after getting drunk in the apartment of a woman named Edna, with a huge wad of cash.  He goes to return it, and finds her dead.  He enlists a dance hall girl, June (Susan Hayward), to help him figure out who murdered Edna, so he doesn't get blamed.  They have until dawn, when he is due on the bus back to Norfolk Navy Yard.  The dead woman was having an affair. Suspects include the man Edna was having the affair with, that man's wife, Edna's creepy brother and a mysterious man wearing white gloves who is following them.

Alex is arrested.  The cab driver who has been driving them around all night (Paul Lukas), confesses to the murder.  He is the father of the woman who's husband was having the affair with Edna.  He murdered Edna so his daughter could get her husband back.  June and Alex have fallen in love. June leaves the dance hall business to go back to Norfolk with Alex.  

Thanks Joseph C!