The Devils did everything they promised they would Saturday night.

They had increased offensive zone time. They generated offense. They were much improved.

Still for all of their improvements, the Devils head to Los Angeles trailing the Kings in the series two games to none after losing 2-1 in overtime. Jeff Carter’s wrist shot from the high slot 13:42 into overtime was the game-winning goal.

Carter walked around Andy Greene at the half boards and threw a backhander that Martin Brodeur stopped. Carter corralled the rebound behind the net, carried the puck to the middle of the ice and fired a shot that beat a sprawled Brodeur.

“It [stinks]. There’s no way around it,” Adam Henrique said of the consecutive overtime losses. Last night’s match marked the first time since the Toronto Maple Leafs-Montreal Canadiens 1951 Stanley Cup final in which the first two games of the final went to overtime. Every game of that series was decided in overtime.

Game 3 is Monday night at the Staples Center.

The Devils fired 33 shots at Jonathan Quick and took 67 attempted shots over the course of Game 2’s 73:42. Yet Quick turned away 32 shots and was not made to work especially hard. He did not have to fight through screens nor deal with much traffic.

“We all need to do a better job of creating offense,” Zach Parise said.

Added Stephen Gionta: “I think we need to keep getting traffic to the net, keep getting pucks to the net and hopefully the bounces will go our way.”

What the Devils could really use at some point in the next two games is a lead. The Kings have not trailed in either game.

Last night it was Drew Doughty who opened the scoring 7:49 into the game with a spectacular end-to-end rush that was reminiscent of Scott Niedermayer’s goal in Game 2 of the 1995 Stanley Cup final.

Doughty weaved through all three zones before wiring a shot that beat Brodeur blocker side.

“I actually remember Niedermayer when he played in New Jersey having a couple end to enders. He was an unbelievable player here; everywhere he played. I always wanted to emulate him. He always scored some highlight goals that I remember,” Doughty said of Niedermayer before describing his goal.

“I just saw some ice in front of me [and] decided to skate with the puck,” Doughty said. “I don’t know who the D man was, but I tried to use him as a screen. Marty has that quick glove so I went blocker side. I didn’t even know it went in actually, but luckily, it did.”

Despite the Devils having outshot the Kings, 33-32, Brodeur was the reason the game reached overtime. The 40-year-old was the Devils’ best player as he kept his team in the game in the first 40 minutes.

“He’s always played well,” Henrique said of Brodeur. “He’s a big reason why we’re here. He kept us in it tonight and gave us a chance to win.”

Ryan Carter drew the Devils even at 2:59 into the third with his fifth goal of the playoffs. The Devils surged following the fourth liner’s goal, but were unable to take advantage of their chances and now head to Los Angeles needing to win one game to bring the series back to the Rock.

There is not a lot to be positive about going into Games 3 and 4, but Devils head coach Pete DeBoer is optimistic.

“We just played a much better game tonight. We spent more time in their end of the ice, got more shots through to the net, got more point shots,” DeBoer said. “It wasn’t an adjustment. That’s our game. We just executed better tonight than we did Game 1.”

Yet they are halfway home for the summer.

Follow NHL beat writer Denis Gorman on Twitter @DenisGorman.