As an end for Yale, where he was also an outstanding baseball pitcher, Stagg was chosen for Walter Camp's first All-America football team (1889). He then attended the International Young Men's Christian Association (YMCA) Training School, afterward Springfield (Mass.) College; there he both played and coached football and became one of the first enthusiasts of basketball, which was invented by James Naismith at the Springfield school in 1891. On Jan. 18, 1896, Stagg's University of Chicago team defeated the University of Iowa in the first intercollegiate basketball game with five players on each side.

During Stagg's 41-year tenure (1892–1932) as football coach at Chicago, the Maroons won six Western Conference (Big Ten) championships outright (1899, 1905, 1907, 1908, 1913, 1924) and tied for another (1922). They were undefeated and untied in two seasons (1905, 1913) and undefeated but tied at least once in two other years (1899, 1908). For his Chicago teams he devised the end-around play, the man in motion, the huddle (also credited to Bob Zuppke, coach at the University of Illinois), the shift (later employed with great success by Knute Rockne at the University of Notre Dame), and the dummy for tackling practice. After his enforced retirement from Chicago at the age of 70, he was head coach at the College (now University) of the Pacific, Stockton, Calif. (1933–46); advisory coach at Susquehanna University, Selinsgrove, Pa., under his son, head coach Amos Alonzo Stagg, Jr. (1947–52); and advisory coach at Stockton Junior College (1953–60).