New York (12-11-7) finishes third in the Eastern Conference and opens a two-game Eastern Conference semifinal series Oct. 27 against New England.
By beating Chicago, LA (9-13-7) will tie it with 37 points and win the head-to-head tiebreaker, 2-0.
Kansas City already has 37 points and if it gets a point against Dallas Saturday will finish ahead of the Galaxy regardless of the Fire result.
Colorado, with 35 points, can also outdistance the Galaxy by beating Real Salt Lake. But if Kansas City loses, and the Galaxy wins, LA will beat both Chicago and the Wizards in the head-to-head tiebreakers and qualify as the eighth seed even if it finishes behind Colorado.
Landon Donovan scythed through the Red Bulls a few times and Cobi Jones, played his last regular-season home game, worked some nice combinations with Donvan and right back Chris Klein to produce chances. One low ball from Klein to the near post produced a good Pete Vagenas shot that keeper Jon Conway, who struggled through some anxious moments, palmed to safety.
Troy Roberts headed a Donovan corner kick past Conway in the 15th minute, and as the celebrations began to ebb and confetti settled on the field, Altidore nailed his ninth goal of the season from a precise Dave van den Bergh cross. Juan Pablo Angel, active but not all that incisive for most of the match, had played the ball up the left flank for van den Bergh.
Angel cut inside Roberts late in the first half and got a good look at goal but fired his shot high. Joe Cannon stopped a fierce shot from Dane Richards, and Donovan dribbled a shot wide.
Altidore glided behind the Galaxy defense in the final minutes and could have killed the playoff suspense once and for all, but he drilled his shot a yard low past the far post.
A match that could have gone either way ended up even, and extends the Galaxy quest for the final three days of the season.
Los Angeles 1 New York Red Bulls 1
Goals: Roberts (Donovan, Vagenas) 15; Altidore (van den Bergh, Angel) 16.
Los Angeles -- Cannon, Klein, Jazic, Roberts, Randolph, Jones, Tudela, Vagenas (Beckham 68), Martino (Glinton 57), Donovan, Pavon (Buddle 64),
New York -- Conway, Mendes, Parke, Freeman, van den Bergh (Leitch, 46), Richards, Vide, Altidore, Stammler, Angel, John Wolyniec (Ubiparipovic, 70),
Yellow cards: Los Angeles -- Martino 54; New York -- Richards 63.
Referee: Kevin Stott