My Favorite Martian (1963) : 1x31

Mrs. Brown's niece, Paula Clayfield, comes for visit. A former child prodigy, Paula has always relied on her brains to mask insecurities in her personal appearance. Despite her Plain Jane looks, Paula does have a boyfriend, Dr. Edgar Edgarton (her intellectual equal), with whom she has an "understanding" - they have a commitment to each other shy of a formal engagement. Paula notices Martin's sketches for a space ship, and insists on helping him to refine his design. Later, she also notices in Martin's possession a piece of a Martian alloy (something not available on Earth) to which she states she cannot identify its contents. These probings of course hinder Martin's progress in fixing his space ship as well as his hiding his Martian identity, so Martin asks a reluctant Tim to ask her out to keep her otherwise occupied. After Paula and Tim's first "date", Paula confides to Martin that Tim seems disinterested, which is indeed the case. So to get Tim to ask Paula out again, Martin transforms her into a ravishing beauty without her knowledge. This transformation does the trick on Tim, who continues to take Paula out and eventually asks her to marry him, which convinces her that she can be and is beautiful. Edgar comes for a visit, and after some time he notices the transformation in her appearance, which solidifies their commitment to each other. In the meantime, Paula has accidentally taken Martin's alloy, which she and Edgar are going to get tested. Martin's Martian identity would then be exposed, that is unless Martin and Tim can get the alloy back beforehand.