Born in Birmingham, Alabama, Sullivan began his athletic career as a three-sport star at Birmingham's John Carroll Catholic High School. Although a talented baseball and basketball player, he chose to play football for Auburn University where he would become the starting quarterback in 1969 under the tutelage of head coach Shug Jordan. Over the next three seasons, the 6' tall and 190 lb. Sullivan would break school and NCAA records for passing while leading the team to a 26-7 record. In 1970, he led the NCAA in total offense with 2856 yards and set an NCAA record for most yards per play with 8.57. In his career, he was responsible for 71 touchdowns (53 passing/18 rushing) to tie the NCAA record. In his senior season, Sullivan completed 162 passes on 281 attempts for 2012 yards and 20 touchdowns. This performance was enough to edge out Ed Marinaro for the 1971 Heisman Trophy. Also an excellent student, Sullivan was named an Academic All-American and graduated with a bachelor's of science in business administration in 1972.

After college, Sullivan had a short professional football career playing first with the Atlanta Falcons from 1972 to 1976 and then the Washington Redskins in 1976 and 1977. He left football to enter private business in Birmingham where he worked in insurance and as a tire company executive. Sullivan also spent five seasons doing radio color commentary for Auburn football games before joining the staff at Auburn in 1986 as quarterbacks coach under head coach Pat Dye. He worked with AU quarterbacks Jeff Burger, Reggie Slack, and Stan White during his six years at Auburn.

On January 2, 1992, Sullivan became the 27th head football coach of Texas Christian University, inheriting a probation-wracked team. After two losing seasons, he led TCU to a 7-5 mark in 1994 to win a share of the Southwest Conference championship. Following the 1994 season, prior to the Horned Frogs' appearance in the Independence Bowl vs. the University of Virginia, Sullivan agreed to become the head coach at LSU. However, LSU officials could not negotiate a buyout of Sullivan's TCU contract, and the Tigers hired Vanderbilt University coach Gerry DiNardo three days later.

The next season produced another winning record of 6-5 before TCU joined the Western Athletic Conference in 1996 and fell once again on hard times. Losing seasons in 1997 and 1998 resulted in Sullivan's resignation in November 1998 with an overall record of 24-42-1. However, he is best noted for recruiting LaDainian Tomlinson to play at TCU.

In January 1999, Sullivan became the offensive coordinator and quarterbacks coach of UAB. He helped develop Darrell Hackney into the best quarterback in UAB history who was able to make it to the NFL as an undrafted free agent picked up by the Cleveland Browns.

After neck surgery in September 2003, Sullivan was diagnosed with throat cancer (squamous cell carcinoma) and began chemotherapy and radiation treatments in December. In April 2004, doctors told him he was clear of cancer cells but he continues to be monitored for recurrence. Sullivan missed only one game in the 2003 season due to treatment but lost around 50 pounds over the course of his treatment.

On December 1, 2006, Sullivan was named head coach at Samford University, replacing Bill Gray.

Sullivan is married to the former Jean Hicks of Birmingham and they have three children — Kim, and twins Kelly and Patrick, Jr.