Baughan was selected in the second round of the 1960 NFL Draft by the Eagles as the 20th player chosen overall and became an immediate starter for the team at right side linebacker. Baughan played the next 10 years in the NFL and was voted all-pro seven times. At the conclusion of his rookie season, the Eagles won the 1960 NFL Championship, the last title for the franchise until their victory in Super Bowl 52 over the New England Patriots. Baughan was selected to the Pro Bowl for the first of nine times that year, finishing with three interceptions. All told, Baughan would make the Pro Bowl five out of six years during his time with the Eagles. During a December 12, 1965 in a game against the Pittsburgh Steelers, the Eagles intercepted a team-record nine passes en route to a 47-13 win over the Steelers. Six of those points came courtesy of Baughan when he returned a first quarter interception by Steelers quarterback Bill Nelsen 33 yards for the lone touchdown of his NFL career. By 1966, the number of games the Eagles won had sharply declined and Baughan decided that he wanted out of Philadelphia. However, George Allen, who was entering his first season as an NFL head coach with the Los Angeles Rams, won the right to Baughan's services by sending two players to the Eagles in return. Baughan and Allen would develop a strong relationship, spending extensive time studying game film together. Baughan would later state that he learned more about football from Allen than anyone else. Baughan was chosen to be the Rams defensive captain and was in charge of signal calling for the unit. He was selected for the Pro Bowl in each of his first four seasons with the Rams and was also named 1st Team All-Pro three times. After an injury-plagued 1970 season, in which he played in only 10 games, Baughan retired from the NFL. From 1972 to 1973, he was an assistant coach and defensive coordinator at Georgia Tech. In 1974, Allen, now the head coach of the Washington Redskins, talked Baughan into a brief return to the NFL as a player-coach for the Redskins. At the conclusion of that season, Baughan retired. He finished with 18 interceptions and 10 fumble recoveries in 147 games played.
Coaching career
From 1975 to 1982, he was a defensive coordinator for the Baltimore Colts and Detroit Lions. During his time with the Colts, the team won three straight AFC East divisional championships from 1975 to 1977. He became head football coach at Cornell University in 1983, and his 1988 team was co-champion of the Ivy League. It was Cornell's first championship since 1971. Baughan was forced to resign as head coach at Cornell after information surfaced about an affair he had with an assistant coach's wife. Baughan then returned to the NFL for stints as an assistant with the Minnesota Vikings, the Tampa Bay Buccaneers and, finally, the Baltimore Ravens. He retired from coaching in 1998.