The Kings had chances to extend the lead, but Brodeur, who was the difference in the Devils' victory over the rival Rangers in the conference finals, made three good saves. The best stop by the 40-year-old, three-time Cup winner came on the opening shift of the second, when he blocked Kopitar point blank on the edge of the crease.
Kopitar, of course, would get one past Brodeur much later in the evening.
Brodeur also stopped forward Jeff Carter from in close and made a big pad stop on Penner in the second.
The Devils were held without a shot for more than 14 minutes of the period before Parise was credited with one on a short-handed attempt in which the puck rolled off his stick into the crease.
Quick, who wasn't very busy in the first two periods, made his best save with a glove stop on Zubrus from the left circle after a turnover.
However, New Jersey managed to tie it on Volchenkov's strange goal.
The nation grieved for those hurt, killed and affected by the Boston Marathon bombings. After one of the suspects was caught on Friday — following a day-long lockdown and manhunt — sports returned to Boston over the weekend.
The tally came just after Quick got into a tussle with Parise in the crease, and refused to let the Devils' captain get up after he fell as Parise lost his helmet.
"I think we're going to have to find another level," Devils coach Peter DeBoer said. "We were a little tentative, as was expected for a Stanley Cup final. I think we got better as the game went along, but you have to play 60 minutes against that team.
"We have to be better than we were tonight."
NOTES: Less than a minute into the game, the chant of "BEAT L-A" echoed through the arena. ... Doug O'Neill, the trainer of Kentucky Derby and Preakness winner I'll Have Another, was on hand, as was New York Giants offensive lineman Chris Snee and New York Jets coach Rex Ryan. ... Volchenkov's goal was his first in the playoffs since Game 3 of the 2007 Stanley Cup finals when he played for Ottawa against Anaheim. ... Kopitar's goal was his second OT winner in the postseason. The other was in 2010 at Vancouver. He has 12 points in the last nine games, including six goals. ...The was the first Game 1 of the finals that went to overtime since 2002, when the Carolina Hurricanes defeated the Detroit Red Wings 3-2 at Joe Louis Arena on a goal by Ron Francis, just 58 seconds past regulation.
PHT: After the Rangers and Bruins face off in Game 3 of their series (7:30 p.m. ET; Live Extra, NBCSN), the Kings and Sharks play (10 ET; Live Extra, NBCSN) Game 4 of theirs.
Video: NHL from NBC Sports
Highlights: Red Wings top Blackhawks in Game 3
The Detroit Red Wings returned home tied at one in their Western Conference semifinals series with the Chicago Blackhawks. After a physical, but scoreless first period that was dominated by the Blackhawks, the Red Wings jumped out to a two goal lead by scoring twice in 31 seconds. Detroit ended up winning the game 3-1 and now have a 2-1 lead in the series.
Check out photos from the Kings' Stanley Cup victory parade in LA.
Stanley Cup playoffs
Check out photos from the NHL postseason action.
Stanley Cup winners
A look at the teams that have earned the right to hoist Lord Stanley's prize since 1965.
Some of Hollywood's hottest celebrities take in NHL games.
Check out the ice girls from around the National Hockey League.