It was a fast start from the Patriots at the Gillette Stadium as the hosts kicked off the scoring inside two minutes when Tom Brady's 49-yard pass landed in the safe hands of Vereen, who gave his side an early lead.
However, both sets of defenses would improve after that point, and it would be the Jets who benefited as Nick Folk sent over field goals either side of punts from the home team.
The pattern continued early in the second quarter as New York edged into a 9-7 lead with another successful kick from Folk.
Brady quickly found his form again to drive the Patriots forward with a 10-play drive which resulted in a short pass finding Vereen for the second touchdown of the night.
The final New York drive of the first half ended in more frustration as the visitors were forced to settle for a fourth field goal from Folk.
However, a late spell of pressure from the Patriots ended with Stephen Gostkowski's field goal restoring their five-point lead.