Mikey Anderson put Los Angeles back in front 3-2 at 3:07, scoring his first goal of the season on a shot from the blue line.
Viktor Arvidsson made it 4-2 at 3:17 on a one-timer in the right circle off a pass from Trevor Moore.
"Actually, after they scored, I thought the response from the bench was really good," Durzi said. "A lot of guys just talking it through, saying let's bounce back. Good energy, guys really showed it. To get two in one shift was huge. Feeding off that, building off that, I thought the guys responded well."
Kopitar scored at 4:30 to make it 5-2.
"To come back and put those three goals together was powerful," McLellan said. "It deflates the opposition quickly, and guys made good plays. Confident plays."
Durzi scored on a shot from the right point at 18:20 for the 6-2 final.
"My experience of coaching in this league is when you go through it, an 80-plus-game schedule, that some nights it's a struggle, and this was one of them for us," Sullivan said.
Brown put the Kings ahead 2-1 at 14:32 of the second period on the power play. Durzi's shot deflected off Moore, and Brown was able to collect the loose puck and score on a wrist shot from close range to reach the milestone.