Last season's runners-up were on track for all three points at Columbus Crew Stadium until the hosts' substitute Ethan Finlay found the back of the net two minutes from time.
Real Salt Lake have drawn two and lost one of their past three games, since edging the Colorado Rapids on May 17.
Jeff Cassar's Real Salt Lake are still second in the West, four points adrift of the Western Conference-leading Seattle Sounders after 14 games, while the Crew are fourth in the East.
Both teams were far from full strength due to rotation and FIFA World Cup duty.
The Crew were without Costa Rican duo Giancarlo Gonzalez and Waylon Francis, who are both away on international duty, while midfielder Will Trapp failed to recover from a knee injury.
As for Real Salt Lake, they were missing key United States internationals Kyle Beckerman and goalkeeper Nick Rimando.
Star striker Alvaro Saborio also missed the game after injuring his foot whilst in camp with Costa Rica last week.
Despite the absence of a number of first-team regulars, the match provided entertainment and Columbus should have had a goal in the 11th minute.
Columbus were awarded a penalty after Agustin Viana was brought down by Rich Balchan but star striker Federico Higuain failed to convert the spot kick.
That would be the highlight of the match until Real Salt Lake finally broke the deadlock nine minutes into the second half.
Abdoulie Mansally shot from long range and Luis Gil was on hand to tuck away the rebound as the visitors hit the front.
Just as Real Salt Lake were preparing to celebrate a much-needed win, Finlay came off the bench to break their hearts in the 88th minute - his third goal in four games.
Despite drawing, Real Salt Lake remain three points clear of Colorado Rapids, who played out a goalless draw at home to Chicago Fire.
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