After graduating from college, Curtis was selected by the Bengals in the 1st Round of the 1973 NFL draft (15th Overall). He made the starting lineup as a rookie and had a superb season, recording 45 receptions for 843 yards and 9 touchdowns, an average of 18.7 yards per catch. Curtis continued to be a major contributor for the Bengals until his retirement after the 1984 season.
Although he never reached the 1,000 receiving yards milestone during a season, he was known as a superb clutch player and excelled at gaining extra yards after making a catch. In 1974 and 1975, he averaged more than 21.1 yards per reception. He was a Pro Bowl selection 4 times (1973-1976) and was selected 2nd Team All-Pro for 3 consecutive seasons (1974-76). Curtis assisted the Bengals to a Super Bowl appearance in the 1981 season and had a solid performance in Super Bowl XVI, catching 3 passes for 42 yards.
In his 12 NFL seasons, Curtis recorded 416 receptions for 7,101 yards and 53 touchdowns, while also gaining 76 rushing yards on 25 carries. His 17.1 yards per catch average is a Bengals record and his 7,101 receiving yards was a franchise record until broken by Chad Johnson on September 16, 2007. His 53 touchdown receptions were a Bengals record until surpassed by Carl Pickens in the late 1990s