Hayes' first two seasons were most successful, during which he led the NFL both times in receiving touchdowns with 12 and 13 touchdowns, respectively. In 1966 Hayes caught six passes for 195 yards against the New York Giants at the Cotton Bowl. Later, in the Dallas Cowboys-Washington Redskins match-up, Hayes caught nine passes for 246 yards (a franchise record until Miles Austin broke it with a 250-yard performance on October 11, 2009, against the Kansas City Chiefs). Hayes' speed forced other teams to go to a zone since no single player could keep up with him. Spreading the defense out in hopes of containing Hayes allowed the Cowboys' talented running game to flourish, rushers Don Perkins, Calvin Hill, Walt Garrison and Duane Thomas taking advantage of the diminished coverage at the line of scrimmage. In the 1967 season, Hayes led the NFL in punt return yards, and went on to set an NFL playoff record with 141 punt return yards in Dallas' 52-14 win over the Cleveland Browns. Hayes also caught 5 passes for 145 yards in that game, including an 86-yard touchdown catch.