The marquee matchup between Major League Soccer's highest-profile teams missed some of its usual luster without Henry, the French player expected to be sidelined up to one month because of a strained hamstring
Still, New York was able to piece together a morale-boosting win over its West Coast rival.
''It's definitely big. It's good for the team spirit,'' said defender Markus Holgersson, wearing the captain's band in place of Henry. ''We're fighting for each other.''
Henry had been enjoying a sensational season when he was injured in a 1-0 win over New England on April 28. He has nine goals this season.
Lindpere scored in the 19th minute and the Red Bulls held on to beat the Los Angeles squad that knocked them out of playoffs last season en route to the title.
''We always create chances,'' Holgersson said. ''And when we defend like this, we are a strong team.''
New York improved to 5-3-1, while Los Angeles dropped to 3-5-1 with a second consecutive loss.
The Galaxy were again plagued by an inability to score, succumbing to a second straight shutout loss in what has been a disappointing start to the season. They lost 2-0 to Seattle on Wednesday night.
''We keep saying we're not worried about it,'' Galaxy star David Beckham said. ''But there's going to be a point where we need to be worried about it and we're close to that now.''
Henry was one of six New York regulars to miss the match for various reasons. Fellow designated player Rafa Marquez was serving the final game of his three-game suspension for breaking San Jose midfielder Shea Salinas' collarbone three weeks ago.
Red Bulls coach Hans Backe is counting down the days until his squad returns to full strength.
''I think we can survive three, four games like this,'' he said. ''We just have to focus on the defending game.''
The only goal came courtesy of some spotty Galaxy defense.
Connor Lade started the sequence with a pass alongside the sideline to Jan Gunnar Solli. Solli dribbled into the box and placed a pass between two Los Angeles defenders. Lindpere had ample amount of room, using his left foot to beat a charging Bill Gaudette for his first goal of the campaign.
Gaudette was starting for the third straight game in place of Josh Saunders, who is away from the team dealing with a personal matter.
Play in the second half was dictated by the Galaxy, who despite having a number of opportunities failed to level the score. Juninho's rocket shot in the 81st minute from outside the box required a strong save by Ryan Meara. Landon Donovan later had a look from a few yards out, but his shot went directly at the goalkeeper.
Meara was credited with four saves in his second consecutive shutout effort.
''You can't take one play off with those guys because they'll punish you,'' Meara said.
The Galaxy looked to have broken through for the game's first goal in the 13th minute, only to be denied on a fine recovery by Holgersson. After Robbie Keane drew Meara off his line and sent a flick perfectly over his head, the bouncing ball appeared destined for the back of the net before Holgersson ran it down booted it away at the line.
It was the microcosm of another goal-less Galaxy performance.
''Our play is just not good enough, our passing was poor,'' Beckham said. ''We battled for 90 minutes, that's the positive thing. We had our chances tonight, we didn't put them away. I don't think we deserved to win the game anyway. It's another tough one to take.''