The Bears finally got on the scoreboard in the fourth quarter with two field goals from Robbie Gould, each from 30 yards out in a comprehensive victory for the home side.
Giants backup Ryan Nassib tried to pull his side away as he found Henry Hynoski and Preston Parker with touchdown throws, but the Jets kept pace as Michael Vick found Eric Decker for a three-yard score.
Matt Simms then found Greg Salas to fire Rex Ryan's side ahead but Tom Coughlin's men rallied with a one-yard run from Andre Williams while Nassib sealed the win with a 31-yard touchdown pass to Corey Washington.
Brady found Vereen with a six-yard strike in the third quarter, and backup Jimmy Garoppolo then threw a strike to Taylor McCuller to give the Patriots a 30-point advantage. The Panthers got on the board late when DC Jefferson hauled in a three-yard pass from Joe Webb.
Eddie Lacy gave the home side the lead with a one-yard run, but Maurice Jones-Drew got the Raiders back on level terms with a 40-yard run. In the second quarter, Green Bay took command as Aaron Rodgers threw touchdown strikes to Jordy Nelson and Andrew Quarless.
A field goal from Mason Crosby and a touchdown from Alex Gillet all but sealed the victory, although the Raiders came back late on through two passing touchdowns as Matt McGloin found Brice Butler twice in the endzone to make the scoreline respectable.
Reggie Bush got the Lions off to the perfect start as he ran in a 86-yard score after powering through the line. The Jaguars brought themselves back into the match with two field goals from the boot of Josh Scobee and Kasey Redfern.
Rookie quarterback Blake Bortles then put his side ahead with a 13-yard touchdown pass to Allen Hurns, but Detroit stole the game at the end as George Winn went over the goalline from one-yard out to seal the victory.
Full NFL pre-season results:
Seattle Seahawks 34-6 Chicago Bears
New England Patriots 30-7 Carolina Panthers
New York Jets 32-24 New York Giants
Green Bay Packers 31-21 Oakland Raiders
Detroit Lions 13-12 Jacksonville Jaguars