Stanfill was a 6'5" defensive end with the University of Georgia Bulldogs when drafted by Miami in the first round of the 1969 NFL Entry Draft, with the 11th overall pick. He wore the number 84 jersey throughout his Dolphin's career.
In Stanfill's rookie 1969 season, he started each of the 13 games in which he appeared at the right defensive end position, a spot he would retain throughout his NFL career. He made a splash right away on Miami's 3-10-1 season, securing approximately 61 tackles and eight sacks, blocking a field goal and intercepting two passes, returning them both for touchdowns. He was selected to his first Pro Bowl following the season, one of five Dolphins on the roster. Miami's defense allowed opposing teams an AFL third lowest nine rushing touchdowns on the season.
Stanfill started all 14 Miami games in 1970, making around 56 tackles and six sacks. Miami was much improved, posting a 10-4 record and making their first postseason, losing the wildcard matchup 21-14 to the Oakland Raiders. Miami's defense allowed an AFC low 228 points on the season, opposing teams rushed an AFC low 387 times on Miami, for 1,453 yards.
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In 1971, Stanfill appeared in and started 13 Miami games. He registered approximately 60 tackles, along with 6.5 sacks and three fumble recoveries. In a week nine 24-21 victory over the Pittsburgh Steelers, he made six tackles, recovered a fumble, and collected three sacks. Miami posted a 10-3-1 record, winning the AFC East title. The Dolphins represented the AFC in Super Bowl VI, losing to the Dallas Cowboys 24-3. The Dolphin's defense allowed an AFC second best 174 points on the season and an AFC second lowest 10 touchdowns on the season. Stanfill was selected to appear in his second career Pro Bowl, one of seven Dolphins on the squad (including four future Hall of Famers).
In 1972, Stanfill started each of Miami's games during their perfect season. He would earn his third Pro Bowl selection, one of nine Dolphins on the team. He was also selected as a first team All-Pro, one of 10 Miami players to earn the honor. He made around 70 tackles and 10 sacks, with two fumble recoveries. Miami's defense was legendary, leading the NFL by allowing 171 points scored, 3,297 total yards, and 186 first downs against. They placed first in the AFC by allowing only 1,548 rushing yards for eight touchdowns. Stanfill recorded one sack in each postseason matchup, a 20-14 win over the Cleveland Browns in the Divisional Playoff, a 21-17 victory over the Pittsburgh Steelers in the AFC Title game, and a 14-7 victory over the Washington Redskins in Super Bowl VII.
Stanfill started 13 of his 14 games for Miami in 1973, earning his fourth Pro Bowl, and third in a row. He was one of 12 Dolphins on the team, including four of the "No-Names". Miami finished the season 12-2, the defense was again dominant, leading the NFL by allowing 150 points on an average of 3.7 average yards gained against per play. The passing defense allowed NFL lows with five touchdowns, 3.5 yards per pass play, and 1,290 yards allowed. The team led the AFC with 45 sacks. For his part, Stanfill made around 70 tackles and 18.5 sacks. This includes a week four performance where collected five in a 31-3 victory over the New York Jets. He collected a sack in Miami's 34-16 victory over the Cincinnati Bengals in the divisional playoff. Miami won their second consecutive Super Bowl, downing the Minnesota Vikings 24-7 in Super Bowl VIII.
In 1974, Stanfill started 13 of the 14 games in which he would appear, earning his fifth Pro Bowl selection, and fourth in a row. He was joined by nine other Miami players in Hawaii. He led the team with 10 sacks, also collecting approximately 60 tackles and one fumble recovery. This includes the second five sack performance of his career, a 35-28 victory over the Buffalo Bills in week 10. He also blocked a field goal in Miami's victory. Miami won the AFC East with an 11-3 record, losing in the first round of the playoffs to the Oakland Raiders, 28-26. Miami's rushing defense led the AFC by allowing only seven touchdowns.
1975 would see Stanfill limited by injuries to eight starts in his 13 appearances. He still managed to collect 6.5 sacks and approximately 50 tackles on the campaign as Miami narrowly missed the playoffs with a 10-4 record. Miami's defense was still a juggernaut, allowing an AFC second best 222 points on the season. Miami's pass defense led the NFL with nine touchdowns allowed.
1976 would mark Stanfill's final NFL season. He appeared in every Dolphin's game, but only started three games due to injuries. He led a substandard 6-8 team with four sacks on the season.
Over eight seasons as Miami's starting right defensive tackle, Stanfill collected a (then) Dolphins record 67.5 sacks (unofficially), starting 91 of 109 Miami games.