The teams combined for 74 penalty minutes, including 64 in the second period.
"We held our ground when they had pushes, and when they dropped [the gloves] and came a little harder, we held our ground and fought right back," Coyle said. "It doesn't have to be fights, but that kind of got us more into the game. We played a little more physical and it brought out the best in us."
Devils defenseman Brenden Dillon, who was playing in his 1,000th NHL game, was forced to the locker room after a fight with Dmitri Voronkov at 1:01 of the second period. Dillon returned late in the period but didn't play in the third.
"After [Dillon left], emotions were high," Hischier said. "It was 2-2, the game was open, and some mistakes cost us."
New Jersey also lost defenseman Jonas Siegenthaler, who was given a game misconduct for not having his jersey fastened properly during a fight at 3:58 of the second period.
"I don't like how we handled those situations emotionally," New Jersey coach Sheldon Keefe said. "Obviously, not long after the situation with [Dillon] they scored, so I don't like that. We've got to do a better job of staying in it emotionally, as hard as it might be."
Hischier scored a power-play goal at 1:26 of the first period to give New Jersey a 1-0 lead when his centering pass deflected in off the stick of Columbus defenseman Ivan Provorov.
Palat extended the lead to 2-0 on a wrist shot from the slot at 3:03.
Denton Mateychuk pulled the Blue Jackets to within 2-1 with a power-play goal on a redirection from the slot at 9:54.
The Devils appeared to take a 3-1 lead at 17:08 when Timo Meier scored a power-play goal off a scramble at the right post, but the Blue Jackets successfully challenged the play for goalie interference on Stefan Noesen in the crease.
Monahan then tied it 2-2 at 1:28 of the second period with a wrist shot from the left hash marks during 4-on-4 play.
Coyle converted his own rebound at the left post at 6:40 of the third period to give Columbus a 3-2 lead, and Monahan scored 34 seconds later on a snap shot outside the right post to make it 4-2.