Nil Battey Sannata is a rare film, the kind that will bring tears to your eyes but leave a smile on your face. Apeksha "Apu" Shivlal Sahay (Ria Shukla) is an unmotivated student who has managed to reach her matriculation year in high school despite her lack of interest in studying further. She struggles in mathematics alongside her friends, Sweety (Neha Prajapati) and Pintu (Prashant Tiwari). Her single mother Chanda (Swara Bhaskar), a high school drop-out, works four different menial jobs, which include working as a maid for Dr Diwan (Ratna Pathak).

Troubled by her daughter's rebellious attitude, Chanda narrates her dilemma to Dr Diwan, who suggests that she hire a math tutor for Apu. Chanda is told that in order for her to receive a considerable discount on the tuition, Apu must pass her pre-board math exams. When her mother relays this information to Apu, she replies that she is destined to work as a maid, as Chanda cannot provide financially for any higher education. With the encouragement of Dr Diwan, Chanda enrols in Apu's school so that she can learn math and tutor Apu herself. Apu, however, perceives her mother's actions as embarrassing and continuously ridicules her. Everyone, except for the school's principal Mr Srivastava (Pankaj Tripathi), is oblivious of Chanda's relationship to Apu; she manages to befriend Apu's classmates, including Sweety and Pintu and impresses her teachers with her steady progress. Chanda enlists the help of her quiet and shy classmate Amar (Vishal Nath) to understand math and realizes that the subject becomes easier if it is understood well.

Apu is angered by her mother's success in math, as she herself continues to fail to understand it. Chanda challenges Apu to achieve grades higher than hers in math; if she is successful, Chanda promises to drop out of school. With Amar's help and constant studying, Apu manages to complete the challenge. Her mother is overjoyed but is heartbroken when Apu informs her that she performed well in school with the sole purpose of ensuring her mother's absence at school. In her anger, Chanda breaks her promise and returns to school, performing even better than before, much to Apu's chagrin. After allotting more time to school, Chanda loses one of her four jobs and begins to work at a restaurant because Amar recommends the job.

One night, she is dropped off at home by one of her male colleagues; Apu witnesses this and assumes that Chanda receives financial help from the man in exchange for companionship. She steals the money that Chanda has been collecting to pay for her tuition and spends it all on food and new clothes. This devastates Chanda, who becomes depressed when Apu tells her that the money was not hard-earned. Chanda stops attending school and continues to work with the hope that Apu will join the Indian Administrative Service after she is inspired by a kind District Commissioner (Sanjay Suri). In the meantime, Amar helps Apu realize her mistake by making her witness Chanda working at the restaurant. Apu rekindles her interest in school and begins to treat her mother with respect, having realized that she can perform well if she possesses the will. She brings her mother back to school and the duo finishes their matriculation year together.

With a scenic view of the Taj Mahal, Chanda motivates Apu to always follow her dreams, as they are dependent on effort and not circumstance. A few years later, Apu attends her Union Public Service Commission interview, having passed her examinations successfully. After being asked what inspired her to apply for IAS, she answers that she is inspired by her mother, who now tutors struggling math students free of charge.