Baker then pursued graduate study at the University of Washington under Larry Sandler, receiving his doctorate in 1971.
Baker remained at UW alongside Sandler before working with James F. Crow.
In 1974, Baker began teaching at the University of North Carolina, Chapel Hill.
Stanford appointed Baker as Dr. Morris Herzstein Professor of Biological Sciences in 2001.
He left the university in 2008 for a position at the Howard Hughes Medical Institute's Janelia Research Campus.