Burrough was selected by the New Orleans Saints in the first round (10th overall) of the 1970 NFL draft.[3] He missed much playing time his first season due to minor injuries, catching only 13 passes for 196 yards and two touchdowns. In January 1971, Burrough and fellow Saint player Dave Rowe were traded to the Oilers in exchange for Hoyle Granger, Terry Stoepel, Charles Blossom, and a draft choice to be named later.[4]
Burrough played eleven seasons with the Oilers, from 1971 through 1981. In 1975, Burrough was selected to the Pro Bowl, leading all NFL wide receivers with 1,063 receiving yards, the only receiver to gain more than a thousand yards for the season. He scored eight touchdowns that year, and averaged 20.1 yards per reception. In his book, More Distant Memories: Pro Football's Best Ever Players of the 50s, 60s, and 70s, Danny Jones wrote that Burrough was "one of the most dangerous game breakers in the NFL along with Cliff Branch (Raiders), Mel Gray (Cardinals), and O. J. Simpson (Bills)." Six of Burrough's eight touchdowns were of 50 or greater yards. In a week thirteen game against the playoff-bound Raiders, Burrough caught four passes for 112 yards and two touchdowns, including a screen pass from quarterback Dan Pastorini which he turned into a 68-yard touchdown with his open field running skills.[5]
Burrough was the last NFL player to wear number 00 on his jersey; the league restricted all numbers to between 1 and 89 in 1973 (later expanded to 1 and 99 in 1987), but Burrough and Oakland Raiders' center Jim Otto, both of whom wore 00 at the time, were covered under a grandfather clause for the rest of their careers.[6]
Burrough has the third most receiving yards in Oilers/Titans history with 6,906 and tied for third in receiving touchdowns with 47. He ranks 85th on NFL All-Time Yards per Reception List with 16.9 yards per pass reception.