Scarnecchia began his coaching career in 1970 with his alma mater California Western University as their offensive line coach, a position he held through 1972. From 1973 to 1974, Scarnecchia was the assistant offensive line and assistant defensive backfield coach for Iowa State University. In 1975, he began a two-year stint with Southern Methodist University, first as a graduate assistant before being promoted to offensive line coach upon the hiring of head coach Ron Meyer in 1976. From 1977 through 1978, Scarnecchia served as offensive line coach for the University of the Pacific before spending a year at Northern Arizona University in the same capacity. He returned to Southern Methodist in 1980 as offensive line coach, spending two seasons there before following head coach Ron Meyer to the Patriots.
Scarnecchia joined the Patriots in 1982 as a special teams and tight end coach. From 1989 to 1990, he served on Meyer's Indianapolis Colts' staff as their offensive line coach. Scarnecchia returned to the Patriots in 1991, where he spent two seasons under Dick McPherson again as a special teams and offensive line coach. In 1992, Scarnecchia held the responsibilities of head coach while MacPherson was ill for the final eight games of the season. Under head coach Bill Parcells in 1993 and 1994, Scarnecchia was reassigned as a special assistant. In 1995, Scarnecchia was again reassigned, this time to a defensive assistant. Once Parcells left the team after the 1996 New England Patriots season, and Pete Carroll was hired as head coach, Scarnecchia became the team's special teams coach again. In Carroll's final season with the Patriots, Scarnecchia was reassigned to offensive line coach. New head coach Bill Belichick additionally appointed Scarnecchia as the team's assistant head coach in 2000.
Scarnecchia retired after the 2013 season, and was replaced by Dave DeGuglielmo. Even after retiring as a coach, Scarnecchia still worked with the team; for example, he had private workouts with the two offensive linemen the Patriots drafted in 2014, Bryan Stork and Cameron Fleming. After the Patriots parted ways with DeGuglielmo after the 2015 season, the Patriots and Scarnecchia expressed mutual interest in having Scarnecchia return to coach the offensive line in 2016.
Dante Scarnecchia is the father of former Denver Broncos video director Steve Scarnecchia, who was fired in November 2010 after he was found to have illegally videotaped a San Francisco 49ers walkthrough practice in October 2010. Steve had previously worked in the video departments for the New York Jets (2006–2007) and the Patriots (2001–2004).