The Patriots marched 93 yards to their first score, which came on Irving Fryar's 20-yard reception of a Tony Eason pass.
The Patriots then marched down the field and the first half ended on a 27-yard Gostkowski field goal.
Patriots march to brass bands, and firework displays are held in most cities.
The Patriots marched for five first downs and held the ball for more than eight minutes.
When the Giants turned the ball over on downs, the Patriots marched downfield on a Giants defense that was starting to look fatigued.
The Patriots subsequently marched to the 9-yard line, but Carolina kept them out of the end zone and Adam Vinatieri missed a 31-yard field goal attempt.
Then, after forcing the Jets to punt, the Patriots marched to New York's 1-yard line.
Patriots march to New Orleans.
The Patriots subsequently marched down the field on another long scoring drive, taking 5:06 off the clock.
In the fourth, the Jets again pulled to within seven points, but the Patriots again marched down the field, eating more than six minutes off the clock.