Sergey Ivanovich Krivolutsky was born in 1869 in the village of Kurdyuki in the Kirsanov district to a deacon's family. His parents sent him to the Tambov Spiritual School, but soon he began taking painting lessons from a local artist I.I. Gladyshev, a graduate of the Academy of Arts. Later, he moved to Kozlov, where he studied in the workshop of M.F. Yuryev. In 1891, Krivolutsky entered the Moscow School of Painting, Sculpture, and Architecture. After graduating in 1896, he moved to St. Petersburg and became a free student at the Higher Art School of the Academy of Arts in the workshop of Professor V.E. Makovsky. After a trip abroad, he returned to the Tambov province and taught for several months at the church-teacher seminary in the village of Novikovo in the Kozlov district.

In October 1900, Krivolutsky opened free evening drawing classes, which soon closed. In January 1901, the newspaper "Tambov Provincial News" reported that classes resumed in the icon painting workshop of M.F. Yuryev under Krivolutsky's guidance. In addition to drawing from originals, plaster, and life, he lectured on perspective and anatomy. The school had up to 15 students, each paying 10 rubles a month.

Despite the popularity of the exhibitions, the Academy of Arts did not support Krivolutsky. The school was not profitable, and the artist was forced to invest his own funds. His financial situation worsened, and in 1906 he closed the educational institution. Some students continued their studies at other art schools, including A.M. Gerasimov.

In 1909, Krivolutsky moved with his family from Kozlov to Moscow, where he took on random commissions. In 1919, he returned to the Tambov region and settled in his native Kurdyuki (now the Inzhavinsky district of the Tambov region). In addition to portraits, he tried his hand as a decorator, designing the play "At the Bottom" at the Kirsanov City People's Theater.

S.I. Krivolutsky is the author of the paintings "At the Village Artist" (Tver Art Gallery), "Family and Art" (Research Museum of the Academy of Arts, St. Petersburg), and "In the Night Shelter" ("At the Bottom") (Tambov Regional Local History Museum).

The artist passed away in the summer of 1922 in Kurdyuki.