"The Power of One" follows an English-speaking South African boy named Peekay from 1939 to 1951. The story begins when Peekay's mother has a nervous breakdown, and Peekay ends up being raised by a Zulu wet nurse, Mary Madoma; who eventually becomes his nanny. At a young age, Peekay is sent to a boarding school. As the youngest student attending the school, he is frequently harassed. The students call him Pisskop (meaning piss-head) and rooinek (redneck—a name given to the British during the Boer War) among other names. This continues with an older boy, the Judge, and his partners who further punish him for his frequent bedwetting with verbal and physical abuse. The Judge is a Nazi sympathizer, and he has a hatred for the English, proclaiming that Hitler will march the English out to sea. The Afrikaans woman who runs the boarding school does not console him and walks around threateningly with a whip.
After Peekay returns home after his first year at the boarding school, his nanny calls a medicine man called Inkosi-Inkosikazi to cure his bedwetting. Inkosi-Inkosikazi not only succeeds, but also leads Peekay's mind to a place where there are three waterfalls and ten stepping stones, where Peekay can always "find" him. The next school year, Peekay returns with a magic chicken of Inkosi-Inkosikazi's and a different paradigm, called the power of one. Peekay is excellent in his studies, but maintains a camouflage to hide it from his fellow students and teachers. He finds that this is a good way to beat the system and avoid unnecessary abuse. As the punishments from the Judge continue to get worse, Peekay ends up doing the Judge's math homework. At the end of the year, the Judge forces Peekay to eat feces, and kills his beloved chicken. He looks forward to arriving home to his nanny, but has been informed there has been a change in plans. He will be travelling to a town called Barberton, where he will meet his grandfather.
On the train ride to Barberton, Peekay meets Hoppie Groenwald, who shows Peekay his boxing gloves. Hoppie is a boxing champion, and he invites Peekay to watch him box during a stop in the ride. It is there that Peekay is inspired to be the welterweight champion of the world. Hoppie teaches Peekay the phrase "First with your head, then with the heart," a phrase which Peekay commits to memory. At Barberton, Peekay sees his mother again. She has returned from the mental institution and converted to being a born-again-Christian. He learns that his mother had left his nanny because she refused to convert. His mother also tries to convert him, but he tells his mother that the Lord is a "shithead." Retreating to the hills behind his home, Peekay meets a German professor, Karl von Vollensteen, to whom Peekay refers to as "Doc." Doc is a music professor and botanist who collects cacti and has his own cacti garden. Doc and Peekay become close friends, and he offers Peekay piano lessons. When World War II breaks out, Doc is taken into the Barberton prison for being an unregistered alien. Peekay visits him every day for piano lessons, and attends the prison's boxing squad. A prisoner whom Peekay becomes friends with, Geel Piet, teaches him to box, and Peekay leads the team to a victory. Later, Peekay develops great sympathy for the prisoners and arranges Doc and Geel Piet a letter-writing service and a tobacco distribution service. This makes Peekay very famous among the prisoners, and they call him the great chief "Tadpole Angel." One of the wardens discovers that some suspicious activity has been going on, and one night, Geel Piet is murdered in the gym.
The War ends, and Doc finds himself free again. Ms. Boxhall, the librarian and a Jewish schoolteacher, Miss Bornstein, work with Doc to further teach Peekay intellect with many activities such as science, literature and chess. He passes his Royal College of Music exams and earns the best under-twelve boxer in the region. With the help of his guides, Peekay is accepted into the prestigious Prince of Wales school in Johannesburg.
At the Prince of Wales, Peekay partners with the son of a Jewish millionaire, Morrie (Hymie in non-American versions) Levy. They pull off many "scams" to earn money and Peekay joins the school's ailing boxing team. Morrie becomes Peekay's manager and they pull off the first win of the school in many years. Peekay then starts boxing lessons with South Africa's famous Solly Goldman. Peekay grows to be a stranger to failure, excelling at academics, boxing and rugby. Near the end of his last year of school, he must face the death of Doc and not earning a Rhodes scholarship, therefore missing his chance to join Morrie (Hymie) at Oxford.
As a result, Peekay takes a year off of boxing and academics and goes to work in Northern Rhodesia's copper mines to "find himself" and build up the muscle to become a welterweight. He takes on the dangerous work of a "grizzly man" as required by all new miners, but continues on to earn double wages, thereby saving enough to attend Oxford. At the mines, he meets a Georgian called Rasputin and they become close friends. When Peekay has an accident in his shaft, Rasputin saves Peekay, but gives his own life up instead. Rasputin names Peekay as his beneficiary; that and his own insurance payout gives him enough to be able to attend Oxford. One night before Peekay leaves the mining camp, Peekay meets his old nemesis, the Judge, in a bar at the mines. The Judge is in an insane rage due to handling mine explosives and tries to kill Peekay. A fight ensues and Peekay puts all he has learned in his life to destroy the Judge. After defeating the Judge, Peekay carves a Union Jack and the initials "PK" over the Swastika in the Judge's arm.