John Nelson Russell Score was born on April 21, 1896 to John and Katie Marie (Ebrecht) Score in White Church, Missouri. He earned his B.A. degree from Scarritt-Morrisville College in Missouri in 1914, followed by a B.D. degree from Emory University in Georgia in 1916. Furthering his education, he attended New College, Edinburgh, Scotland, and the University of Edinburgh in 1919. His scholarly pursuits culminated in a Th.D. degree from the Pacific School of Religion in Berkeley, California, in 1924. On January 12, 1921, Score married Margaret Ruth Smith, and they would have one child, John Nelson Rusell Score II.

Embarking on a dedicated career in Methodist ministerial and religious service from 1913, Score held pastorates and assumed various roles of significance in the church, spanning both the United States and Europe. During World War I, Score served valiantly as a chaplain, holding the rank of first lieutenant in the United States Army from 1918 to 1919. Post-war, he continued his service as a chaplain, achieving the rank of captain in the California National Guard (1925–26) and later in the Texas National Guard.

Assuming the presidency of Southwestern University in Georgetown, Texas, on June 1, 1942, Score led the institution with distinction until his passing. Beyond his administrative responsibilities, he contributed actively to the boards of trustees of various Methodist institutions and engaged in scholarly societies and civic clubs.

Score passed away on September 26, 1949 while still serving as University President. He is buried with his wife in the Lois Perkins Chapel on the campus of Southwestern University in Georgetown.