Martinez scored 14:43 into the second overtime, and the Kings won the Stanley Cup for the second time in three years with a 3-2 victory over the New York Rangers in Game 5 on Friday night.
Marian Gaborik scored a tying power-play goal with 12:04 left in regulation for the resilient Kings, who rallied from yet another deficit before finishing off the Rangers in the longest game in franchise history and the third overtime game at Staples Center in this series.
After innumerable late chances for both teams in two nail-biting extra periods, Martinez popped home a rebound of Tyler Toffoli's shot for the Cup-clinching goal. Martinez is becoming a late-game playoff legend after also scoring in overtime in Game 7 against Chicago in the Western Conference finals.
" Fortunately, the rebound came to me and I was able to put it in," Martinez said. " The New York Rangers are a hell of a hockey team. We knew it was going to be a tough series."
Jonathan Quick made 28 saves and Conn Smythe Trophy winner Justin Williams scored an early goal as Los Angeles added a second title to its 2012 championship, the first in the franchise's 47-year history.
Long an NHL afterthought in their warm-weather city, the Kings have turned into a burgeoning dynasty - and they've turned Hollywood into a hockey town with two titles, capped by this showbiz finish.
Chris Kreider scored a power-play goal and Brian Boyle added a tiebreaking short-handed goal late in the second period for the Rangers, who showed no nerves while facing elimination for the sixth time this spring.
Lundqvist stopped 48 shots in another standout performance for the Eastern Conference champions, but the Rangers repeatedly came up one goal short against the Kings despite their goalie's brilliance.
Martinez started the final rush with a pass to Kyle Clifford, who dropped it to Toffoli for a shot. The rebound went straight to Martinez, and the depth defenseman buried it for his fifth goal of the postseason.
" It's a great play by them," Martinez said. " I'm just the benefactor."
The Kings gathered for a huge group hug near the Rangers' net, while coach Darryl Sutter nonchalantly walked onto the ice with almost no celebration. He wore a broad grin when he raised the Cup above his head several minutes later.
Captain Dustin Brown received the Cup from Commissioner Gary Bettman and immediately handed it to Robyn Regehr, the veteran defenseman and first-time NHL champion who never got back in the Kings' lineup after his May 3 knee injury. Regehr handed it to Gaborik, the goal-scoring dynamo and late-season acquisition who won the first title of his 13-season NHL career.
The season hung in the balance for nearly two full overtime periods. Both teams had tantalizing chances, but couldn't convert.
Ryan McDonagh hit Quick's post with a long shot during an early power play. Toffoli rang a shot off Lundqvist's post with 7:15 left, and the Kings trapped New York in its own end for an exhausting stretch late in the period.
Kreider got a breakaway in the final minute after Drew Doughty fell down, but he missed the net.
A few minutes after Carter's tip shot hit Lundqvist's post early in the second overtime, the Rangers put a tipped slap shot off Quick's post during their second fruitless overtime power play.
Rick Nash had an open net moments later, but Slava Voynov deflected the shot just high with the shaft of his stick.
In stark contrast to their rampage through the playoffs two years ago, the Kings earned this Cup with an incredible degree of difficulty.
Game 5 was the Kings' 26th playoff game of the spring, matching the NHL record for the longest postseason run. Los Angeles has played 64 playoff games over the last three years, setting another league record.
With Sutter and a solid veteran leadership group emphasizing consistency, the Kings have calmly handled everything the NHL could throw at them. After fighting through three straight seven-game series to emerge from the tough Western Conference, the Kings won the first three games of the finals, starting with consecutive OT wins at Staples Center on goals by Williams and Brown.
But New York staved off elimination with a 2-1 victory in Game 4 at Madison Square Garden, earning another cross-country trip.
Staples Center was packed well before the opening faceoff with fans eager for another celebration, rocking the arena with chants of " Go Kings Go!" while both teams were still in their dressing rooms.
Los Angeles started out with yet another big-game goal from Williams, who put the Kings ahead with his ninth goal of the postseason on a loose puck after linemates Dwight King and Jarret Stoll applied pressure on Lundqvist.
The Kings never led in their two overtime victories at home earlier in the series. But even after falling behind early, New York showed no semblance of nerves, largely outplaying the Kings in the first two periods.
The Rangers finally equalized when McDonagh found Kreider in front. Boyle then got a stunner after Carl Hagelin got the puck away from Voynov, skating around Doughty and wiring a pinpoint shot into the far top corner behind Quick with 29 seconds left for his third goal in 25 postseason games.
But the Kings showed the same determination that has characterized their entire spring run, and they finally equalized with Mats Zuccarello in the box.
Doughty's long shot hit Lundqvist in the chest and dropped in front of him before Gaborik alertly poked it between his legs for the 14th goal of a spectacular postseason by the Kings' newest acquisition.
Los Angeles' 2012 title run was defined by that raw, eighth-seeded team's improbable dominance, but the second crown was all about these experienced Kings' incredible resilience.
The Kings' core has largely remained unchanged from two years ago, but Los Angeles traveled a long, winding path to win another title after finishing third in the Pacific Division.
The Kings raised the Stanley Cup just over seven weeks after they faced a 3-0 first-round series deficit against San Jose. Los Angeles confidently won four straight elimination games to become the fourth team in NHL history to rally from that deficit, and then won two more elimination games in a second-round series against local rival Anaheim.
The defending champion Blackhawks forced Los Angeles to a seventh game in Chicago in the agonizing Western Conference finals, but Martinez's deflected overtime goal sent the Kings into the franchise's third Stanley Cup finals.
NOTES: Both teams kept the same lineups from Game 4. Sutter never used Regehr, who has recovered from his May 3 knee injury. ... The Kings never led in their two overtime victories at home earlier in the series. ... The 1987 Philadelphia Flyers and the 2004 Calgary Flames also played 26 postseason games, but neither won the Cup.