The Jets Pats rivalry dates back to 1960 and the birth of the AFL. The Jets were originally know as the Titans, and played under that name for three seasons. The 1963 season became the first one for both the franchise as the Jets, and for new coach Weeb Ewbank, who took over for Bulldog Turner.
Jets Titans game stats: http://www.pro-football-reference.com/boxscores/196211300nwe.htm
the jet report