Moore, who was born in Chicago, Illinois, graduated in chemistry from Vanderbilt University in 1935 and received his PhD from the University of Wisconsin in 1938. He then joined the staff of the Rockefeller Institute, spending his entire career there and serving as professor of biochemistry from 1952 onward.

One of the major achievements of modern science has been the determination by Frederick Sanger in 1955 of the complete amino acid sequence of a protein. Sanger's success with the insulin molecule inspired Moore and his Rockefeller colleague, William Stein (1911–1980), to tackle the larger molecule of the enzyme ribonuclease. Although their work was lightened by the availability of techniques pioneered by Sanger the labor involved was still immense until eased by their development of the first automatic amino-acid analyzer.

They inserted a small amount of the amino-acid mixture into the top of a five-foot column containing resin. They then washed down the mixture using solutions of varying acidity. The individual amino acids travel down the column at different rates depending on their relative affinity for the solution and for the resin. It is possible to adjust the rates of travel so that the separate amino acids emerge from the bottom of the column at predetermined and well-spaced intervals. The colorless amino acids were then detected with ninhydrin, a reagent that forms a blue color on heating with proteins and amino acids. A continuous plot of the intensity of the blue color gives a series of peaks, each corresponding to a certain amino acid with the area under the peak indicating the amount of each.

By the end of the 1950s Moore and Stein had not only established the sequence of ribonuclease but they were also able to indicate the most likely active site on the single-chained molecule. For this work they shared the 1972 Nobel Prize for chemistry with Christian Anfinsen.