One of Goodwin's touchdowns was on a 20-yard pass from Lassiter.
Also scoring were fullback Shone Register, who rushed for a touchdown, and running back Vito Luppino, on a 33-yard run.
The defending state champions improved their record to 4-0, and extended the team's win streak to 29 games.
Madison faces Jefferson at home on Oct. 12 at 7 p.m.
1st 2nd 3rd 4th FINAL Madison (4-0) 21
Hackettstown (3-2) 0 0 0 7 7