Tansen is known to be the greatest classical vocalist ever to have existed in India, and was one of the nine jewels (Navaratnas) of Emperor Akbar’s court. Nobody could sing in the city unless he or she could sing better than Tansen. If this was not the case, he or she was executed. Baiju Bawra is the story of an unknown singer, Baiju, who is on a mission to defeat Tansen in a musical duel to avenge the death of his father.
When Baiju is still a child, Tansen's sentry tries to stop Baiju’s father from singing, and in the ensuing scuffle, his father dies. Before dying, he extracts a promise from his son to take revenge against Tansen. Baiju gets shelter from a village priest and while growing up, falls in love with Gauri, the daughter of a boatman. He continues his musical education on his own, but gets so enamoured by Gauri's love that he forgets the promise made to his father.
Later, a group of dacoits raid Baiju's village. With his song, Baiju persuades them against looting the village, but the female leader of the dacoits falls in love with him and asks him to follow them to their fort as a condition for their sparing the village. Baiju leaves with her, leaving the wailing Gauri behind. In the fort, the dacoit leader, who is actually a princess living in exile, tells Baiju how her father’s serfdom had been usurped and she was seeking revenge because the village too previously belonged to her father. The word “revenge” brings all of Baiju's memories back; he leaves the fort greatly agitated, and the princess does not try to stop him.
Baiju sneaks into the Mughal palace, where Tansen is singing. He is dumbstruck by the way Tansen sings, and the sword that was supposed to cut the maestro’s throat fell on the vina, saddening Tansen. He said he could only be killed by music, and the pain that accompanies it. “Dip your notes in melancholy and I’ll die on my own,” he said. Baiju accordingly leaves the palace to learn “real” music.
Baiju remembers that when his father was killed, he was taking Baiju to Swami Haridas. He goes to see the Swami himself and asks for his guidance, informing him of his plan to take revenge against Tansen. Haridas tells Baiju that one must be in love to be a true musician, and thus Baiju must rid himself of all the hatred in his heart, but still gives him a vina and accepts him as his disciple. Baiju again starts his musical training, spending all his time in a Shiva temple, but his vengeful feelings never leave him. Nonetheless, he still reveres his guru, Haridas. After learning that his teacher had fallen seriously ill and was unable to walk, Baiju sings a song that so thrills Haridas that the master gets out of his bed and starts to walk.
Gauri, meanwhile, is so distraught over Baiju's departure that she is about to swallow poison. At that point, the princess who had taken Baiju from the village comes to her and tells her that she knows of Baiju's whereabouts. Gauri meets Baiju and tries to convince him to return to the village so they can be married; Baiju, however, refuses, as he feels he must take revenge against Tansen. At this point, Haridas arrives, and Baiju goes to receive him, once again leaving a crying Gauri behind.
Haridas tells Baiju that in order to be a true singer, he has to feel real pain. Hearing this, Gauri decides to make a venomous snake bite her, thinking that her death would bring enough grief to Baiju that he would defeat Tansen. Baiju sees Gauri's lifeless body and goes mad, with the princess' attempts to get through to him being futile. Baiju instead goes to the Shiva temple and sings a heart-wrenching song condemning the God who had consigned him to his fate; the idol of Lord Shiva even begins to cry at Baiju's grief.
In his delirious state, Baiju reaches Tansen's city, singing the whole way. The residents fear for his life and call him bawra (insane), hence the title of the movie. Baiju is caught and imprisoned, but the princess releases him. However, both of them are caught by Mughal soldiers when escaping, leaving a musical duel with Tansen as the only way to save his life.
Emperor Akbar himself witnesses the competition. For a long time, both the singers prove to be equally good. Then Akbar suggests that whoever could melt a marble slab with his singing would win the duel. Baiju manages to do so and wins the competition, saving his own life and finally avenging his father's death. Tansen accepts his defeat graciously, and is in fact happy that there is someone better than him.
Gauri’s father was deeply upset when he couldn’t locate Baiju. The entire village was by now making fun of Gauri’s and Baiju’s love affair. Her father warned either Baiju be found, or Gauri should marry a village money-lender and in case she refused, he would commit suicide. Gauri couldn’t divulge Baiju’s whereabouts because she didn’t want him to know that she was alive. So she agreed to marry the money-lender.
Baiju came to meet her while she was getting married, but he was on the other side of Yamuna River and the river was in flood. The boatman refused to take him to the other side.
Despite not knowing how to swim, Baiju pushed the boat into the raging waters and started towing it. He started singing and Gauri heard it. She started running towards the bank and everybody ran behind her. When she saw Baiju struggling with the boat, since she knew how to swim, being a boatman’s daughter, she jumped into the water to rescue Baiju. The boat toppled over and after a lot of struggle Gauri reached him. He urged her to go back and leave him because she knew how to swim and he didn’t. Gauri replied that they had promised to be together in life and in death, and she would be content with dying with him. The film concludes with them both drowning.