[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.
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)."
The Oilers won post-season games in the 1978 and 1979 seasons, making it to the AFC Championship both years, but lost to the Pittsburgh Steelers, the eventual Super Bowl champions.
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.