Under the influence of his father, Dorrance entered North Carolina Central University Law School in 1976, later transferring to the University of North Carolina School of Law. That same year, Coach Allen convinced Dorrance to succeed him as the UNC men's soccer coach. From 1977 until 1988 Dorrance compiled a 175–65–21 (.708) record with the team. His greatest success with the men's team came in 1987 when he led them to the Atlantic Coast Conference tournament championship. They beat North Carolina State University 3-2 winning their first ACC tournament. They also went to the NCAA Final Four in 1987 losing to Clemson University 4-1 in the semi final game. That same year he also won the NCAA Men's Soccer Coach of the Year.