Thierry Henry scored for New York in the fourth minute, Landon Donovan countered for Los Angeles in the 41st and the Red Bulls and Galaxy tied 1-1 on Saturday night.
"Last year, I didn't have the feeling that it was a rivalry or that type of game," New York coach Hans Backe said. "But this year, with the (designated players), the power strikers on both teams, it is a special game."
In a showdown between Major League Soccer division leaders, neither team was able to get the go-ahead goal in the second half despite a flurry of chances.
The matchup featured the league's two biggest draws in Henry and David Beckham, stars who transitioned to the United States after brilliant playing careers in Europe.
Beckham said it's not far-fetched for the Galaxy and Red Bulls to meet in the MLS Cup
"We're two great teams," he said. "It would be a nice final, but there's a long way to go before then."
Beckham played a day after he was involved in a minor traffic accident when he rear-ended a stalled vehicle on a Southern California freeway.
Henry opened the scoring when he took advantage of a Galaxy defensive breakdown, knocking the ball home into an empty net for his fourth goal of the season.
Donovan scored the equalizer for the Galaxy (4-2-4) on a header, ending New York's shutout streak at 333 minutes. Beckham sent in a corner kick from the right side to an unguarded Donovan, who finished from 9 yards.
It was only the third goal this season allowed by New York (4-1-3), which had won three straight.
"It wasn't an easy game today, it was a very difficult one," Henry said. "You saw that both sides were tired at the end."
The Galaxy had a pair of first-half chances that could have potentially proved to be the difference.
Juan Pablo Angel, the Red Bulls' career scoring leader in his first season with the Galaxy, finished a header in the 25th minute that was called off as he was flagged for being offside.
Donovan later thought he had put his team ahead in the 43rd minute. Donovan got behind the defence, beat goalie Bouna Coundoul and flicked the ball home to an open goal. But New York defender Tim Ream hustled his way back and made a sliding save just before the ball passed the goal line.
Donovan argued to referees that the ball had crossed the line, while television replays were inconclusive.
"My take is, it should have been a goal," Galaxy coach Bruce Arena said. "It was pretty close."
Both teams stepped up their level of play down the stretch. It resulted in promising opportunities for each side, but no goals.
"This is probably the best you can see in the MLS, this level between two teams," Backe said. "I can compare it with many leagues in Europe that would have been happy to see a game like this with the number of chances and technical level."