Viktor Arvidsson made it 2-0 at 11:35, scoring on a rebound at the bottom of the left face-off circle off a 2-on-1 with Fiala.
Tatar cut it to 2-1 at 16:44 of the second period on a backhand from the slot after Mercer stole the puck behind the net.
Mercer tied it 2-2 on a snap shot from the right hash marks at 2:23 of the third period.
Durzi gave the Kings a 3-2 lead at 15:41 on a shot at the left post off a backdoor pass from Kopitar.
"There's not a lot of teams that come into this building or play against that team that leave with points," Los Angeles coach Todd McLellan said. "On the other side of it, it is disappointing we couldn't get the last 30 seconds done, but we have to give them some credit too. They broke us down and they made a nice play to the net."
The Devils have an NHL-best 21 comeback wins this season; their record is 23 (2017-18).
"I think we've had a great tendency to deal with adversity, hunker down and overcome bad plays," New Jersey coach Lindy Ruff said. "So, to come back from 2-0 ... they're a tough team to generate chances. They're a very well-structured team, so you've got to give our guys a lot of credit."
NOTES:Kopitar, who has scored in four straight games, reached 20 goals for the 12th time, tying Marcel Dionne, Luc Robitaille and Dave Taylor for the most in Kings history. … Los Angeles forward Trevor Moore is day to day after he was a late scratch with an upper-body injury. He was replaced by center Jaret Anderson-Dolan, who had two blocked shots and was minus-2 in 5:35 of ice time. ... Mercer has an NHL career-high 18 goals; he scored 16 as a rookie last season. Mercer tied Hischier (Dec. 28-Jan. 5) and Hughes (Dec. 30-Jan.7) for the longest goal streak by a Devils player this season.