After having been released by the Giants, and playing one season in the Canadian Football League with the Hamilton Tiger-Cats (catching 1 pass for 10 yards), Maynard became the first player to sign with the New York Titans in 1960 (the team was renamed the Jets in 1963). Although scorned by the New York press as an "NFL reject", in 1960, he teamed with Hall of Famer Art Powell to form the first professional wide receiver tandem to each gain over 1,000 yards on receptions in a season, with the pair achieving this milestone again in 1962. Over the next 13 years Maynard put up receiving numbers that would earn him a spot in the Pro Football Hall of Fame in 1987.
Collecting 72 pass receptions in his first year as a Titan, he went on to compile four more seasons with 50 or more catches and 1,000 yards receiving, and held the professional football record for total receptions and yards receiving. A four-time AFL All-Star, he is sixth in all-time pro football touchdown receptions, and is a member of the All-time All-AFL Team.
In 1965 Maynard was teamed with rookie Joe Namath. Maynard had 1,218 yards on 68 receptions and 14 TD's in Namath's first season (Namath had 22 TD passes that year), and in 1968 the duo hooked up 57 times for 1,297 yards (22.8 yards per catch) and 10 touchdowns (Namath had 15 TD's that year). In 1967 where Maynard caught 1,434 of Namath's historic 4,007 passing yards. The receiving yards were a career high for Maynard and led the league; he also had 71 receptions, 10 TD's, and averaged 20.2 yards per catch. His team would go on to win Super Bowl III the following year which was hailed as the first "upset" in Super Bowl history.
One of only 20 players who were in the AFL for its entire 10-year existence, Maynard was also one of only seven players who played their entire AFL careers with one team. Maynard finished his career with 633 receptions for 11,834 yards and 88 touchdowns. His 18.7 yards per catch is the highest for anyone with at least 600 receptions.
Following his NFL career, Maynard went on to participate in many charity sponsored events. He also participated in the coin toss in Super Bowl XXXIII along with his former teammates, in honor of the 40th anniversary of the 1958 NFL Championship, which is also known as "The Greatest Game Ever Played". He was also once named the Grand Marshall in the annual El Paso Thanksgiving Parade that is held every Thanksgiving Day. He currently lives in Ruidoso, New Mexico.