Andy Williams drilled the right upright in the 9th minute and Robbie Russell smacked the left post 3 minutes later.
The draw left RSL four points back of the Los Angeles Galaxy for the top overall record in Major League Soccer's Western Conference with two games to play.
Real Salt Lake (14-4-10) goalkeeper Nick Rimando made just one save for his league-leading 13th shutout. RSL has lost just once in its last 23 games.
Red Bull (14-8-6), which passed the Columbus Crew to take over first place in the Eastern Conference standings last weekend, extended its lead to two points with the draw.
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