After having been released by the Giants, Maynard became the very 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.
In 1965 Maynard was teamed with rookie QB Joe Namath, and would go on to win Super Bowl III the following year which was hailed as the first upset in Super Bowl history.
In 2008, Maynard 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."
Maynard and Namath chat during halftime festivities.
Maynard currently lives in El Paso, Texas.