The 18-year NFL veteran completed 24 of 34 passes for 289 yards in his 257th consecutive start.
The six touchdown passes were a single-game career high for Farve and equaled a Jets' franchise record.
Hall of Famer Joe Namath tossed six scoring passes against Baltimore Colts on Sept. 24, 1972.
Other AFC honors went to Kansas City linebacker Derrick Johnson (defense) and Pittsburgh placekicker Jeff Reed (special teams).
Johnson compiled seven tackles, ½ sack, one interception and one forced fumble in the Chiefs' 33-19 win over Denver.
Reed's 46-yard overtime field goal gave the Steelers a 23-20 victory against the Baltimore Ravens.
Overall, the seven-year veteran and totaled 11 points with three field goals and two extra points. The seventh game-winning field goal in Reed's career lifted Pittsburgh to its second straight 3-1 start.