Act I: Wang Ta, a young Chinese-American man living in his father's house in San Francisco's Chinatown, discusses the problems of finding a wife with his aunt, Madam Liang ("You Are Beautiful") before hurrying off on a blind date. Nightclub owner Sammy Fong arrives with an offer for Ta's immigrant father, Master Wang, a very old-fashioned Chinatown elder. Sammy's picture bride has just arrived from China, illegally, but the shy Mei Li is clearly the wrong girl for Sammy, who already has an assertive girlfriend, a characteristic he likes. Sammy offers to sign the contract over to the Wang family: this would free Sammy from the contract and arrange a suitable wife for Ta. Sammy has taken the liberty of bringing the girl and her father with him; Wang is charmed ("A Hundred Million Miracles") and invites them to live in his home on the understanding that if the proposed marriage falls through, Fong will still be bound to marry Mei Li.
Ta's blind date proves to be the thoroughly Americanized Linda Low, who we will learn is Sammy Fong's girlfriend and a stripper at his club. On the date with Ta ("I Enjoy Being a Girl"), Linda lies to Ta about her career and family. Ta, knowing that Chinese-Americans with college degrees find it hard to get a job befitting their education, plans to go to law school, postponing the likely career struggle by three years. The impetuous Ta asks Linda to marry him. She agrees, but she needs family consent and lies, saying that she has a brother who will approve the marriage. Ta returns home and meets Mei Li, who is immediately attracted to him ("I Am Going to Like It Here"), though Ta is unimpressed. That changes when Ta sees her in a Western dress ("Like a God").
Linda comes to Madam Liang's graduation party from citizenship school with Linda's "brother" (actually the comedian from Sammy's nightclub) and presents herself as Ta's intended, with her "brother" giving his consent for the marriage. The extroverted, Americanized woman is not what Wang has in mind for his elder son, and Wang and Ta argue. Sammy Fong arrives and quickly penetrates Linda's scheme: Linda, frustrated by the five years she has been seeing Sammy, is determined to marry someone, and if Sammy won't step forward, she will settle for Ta. Sammy quickly strikes back by inviting the Wangs, Mei Li and her father to watch the show at his "Celestial Bar" ("Fan Tan Fannie"). Linda does her striptease, realizing too late who is sitting at the best table. Sammy's special guests storm out, except for Ta, who is so humiliated that he does not know what to do. He is led away by childhood friend Helen Chao, a seamstress who fits Linda's costumes for her, and whose love for Ta is unrequited. Linda, goaded beyond endurance when Sammy raises his glass to her, dumps a champagne bucket over his head.
Act II: The drunken Ta spends the night at Helen's apartment ("Ballet"). In the morning, Mei Li delivers Master Wang's coat for Helen to mend and is distressed to see Ta's dinner jacket there. Mei Li jumps to conclusions and leaves horrified. Ta leaves the lonely Helen, totally oblivious to her attempts to interest him. Wang wants the bar and its "evil spirits" shut down; his sister-in-law informs him that free enterprise cannot be shut down, and the two wonder at the foibles of the younger generation ("The Other Generation"). Ta arrives home to admit that his father was right, Mei Li is the girl for him. But now, Mei Li wants nothing to do with him, and the Lis leave the Wang home. Sammy Fong and Linda decide to get married ("Sunday"), but when he goes to the Three Family Association (a benevolent association) to announce Linda as his bride, he finds Mei Li and her father there, and the elders insist that he honor his betrothal to the immigrant girl.
Ta brings Mei Li a wedding gift of a pair of his mother's earrings that she wore on her wedding day and tries unsuccessfully to hide the fact that he is now deeply in love with her. The wedding procession moves down San Francisco's Grant Avenue with the bride, heavily veiled, carried on a sedan chair ("Wedding Parade"). Sammy drinks from the traditional wedding goblet, then offers the goblet to his new bride. Unveiled, Mei Li confesses to Sammy's mother that she cannot marry Sammy as she is an illegal alien – a tactic she learned by watching American television. The contract is void, and that gives both Sammy and Ta the opportunity to marry their true loves, Linda and Mei Li.