The Last Woman on Earth
(1960)

Harold is a rich man who is down in Puerto Rico with his wife, Evelyn, and his young lawyer, Martin.  Evelyn is a tease and a flirt with Martin.  The three go scuba diving, and come up to find the people on the boat dead.  They can not breathe, and have to keep their scuba tanks on for some time. When they return to shore, everyone on the island is dead.  They deduce that for some reason all the oxygen in the world was temporarily depleted, killing all people and animals.

With two men, and one woman, tension mounts. Evelyn and Martin run off together to try to come back to the US on a boat.  Harold chases them and kills Martin.  

Thanks Joseph C!