New York's Pat Leahy kicked field goals of 24, 30 and 35 yards and Johnny Hector ran for two touchdowns in Green Bay.
It was the Jets' first victory after three defeats. Green Bay is 1-3.
New York led, 24-10, at the half. Green Bay's defense stiffened in the second half and the Packers, led by reserve quarterback Randy Wright, began passing well.
Green Bay narrowed the margin to 24-17 on a 35-yard touchdown pass from Wright to wide receiver Phillip Epps.
Al Del Greco made it 24-20 with a 42-yard field goal on the Packers' next possession, which followed a sack of New York's Ken O'Brien by defensive end Robert Brown.
But early in the fourth quarter, the Jets' offense recovered and got Leahy close enough for a 30-yard field goal to make it 27-20.
With 4:04 left, Leahy kicked a 35-yard field goal following an interception of Wright by cornerback Bobby Jackson.
Wright left the game with 2:44 remaining, having injured the same left knee that kept him out for the latter part of his rookie season.
Wright substituted for starting quarterback Lynn Dickey, who was hit in the back on Green Bay's first offensive series when defensive end Marty Lyons sacked him. Dickey said his hands were numbed.