Hamilton took a pass from Pavel Zacha, who won an offensive-zone face-off, and scored from the slot.
"I was just trying to read [the play] and see where the puck was going and jump by my guy, if possible," Hamilton said. "I was able to do that, and 'Pav' made a great pass and I just put it in."
Jack Hughes had two assists, and Nico Daws made 19 saves for the Devils (20-31-5), who were playing the first of a four-game homestand and seven straight against Western Conference opponents.
"We have good speed and we have good skill, and that's a good combination when you're playing 3-on-3 (in overtime)," New Jersey coach Lindy Ruff said. "Give Zacha a lot of credit for going in and winning that face-off for us. We got two or three defensemen with Damon Severson, Ty Smith, Hamilton, who have good offensive instincts to help us out, too."