Domres received several football scholarship offers, but and chose to attend Columbia University in New York City.

In his lone season in the AFL with San Diego, Domres served as the backup to established quarterback John Hadl.

Domres replaced Hadl in fourth quarter the opening game of the season, a 27-9 loss to the Kansas City Chiefs, where he completed six of 14 passes.

In 1970, the AFL–NFL merger became official and the Chargers joined the newly formed American Football Conference in the NFL.

[11] With limited playing time Hadl, Domres requested a trade and was acquired by the Baltimore Colts for John Andrews and a 1973 first-round pick (25th overall–Johnny Rodgers) on August 7, 1972.

[12][13] In Baltimore, Domres replaced Johnny Unitas as the Colts starting quarterback beginning in week six of the 1972 season.

John Sandusky had succeeded Don McCafferty as head coach and was ordered by general manager Joe Thomas to bench the veterans in favor of the younger players.

Unitas threw a 63-yard touchdown pass to Eddie Hinton, his final scoring throw with the team.

[18] After a poor start, Colts' head coach Howard Schnellenberger made the switch to Domres, who led the team for the remainder of the season.

In the weeks before the 1976 season began, the Colts traded Domres to the San Francisco 49ers for a 1978 draft choice (which became Ernie Hughes).