Born in 1899 in czarist Russia of an accountant and a housewife, young Pelageya was the second youngest of four children. She studied at a women's high school in St. Petersburg and went on to Petrograd University (after the Revolution of 1917). Her father died in 1918 so she started to take care of the family by working at the laboratory of geophysics. There she met Nikolai Kochin, and they married in 1925 and had two daughters. The two taught at Petrograd University until 1934, when they moved to Moscow, where Nikolai Kochin took a teaching position at the University of Moscow. In Moskow, Polubarinova-Kochina did research at the Steklov Institute until World War II, when she and their daughters were evacuated to Kazan while Kochin stayed in Moscow to work on aiding the military effort. He died before the war was over. After the war, she edited his lectures and continued to teach applied mathematics. She was later head of the department of theoretical mechanics at the University of Novosibirsk and director of the department of applied hydrodynamics at the Hydrodynamics Institute. She was a founder of the Siberian branch of the Academy of Sciences at Novosibirsk.
She was awarded the Stalin Prize in 1946, was made a Hero of Socialist Labor in 1969 and received the Order of the Friendship of Nations in 1979. She died in 1999 a few months after her 100th birthday.