The draw was enough to keep RSL ahead of Colorado (11-9-13) in the Western Conference. It was Colorado's fourth scoreless tie of the season, giving the Rapids 46 points.
"It was real disappointing," Colorado coach Gary Smith. "We played as good a first half as we could against a very good team, but then a little bit of snap went out of some of our pressure in the second half."
Real Salt Lake (15-11-7) has 52 points with a game to play. The team is 0-4-1 in its past five games.
"We did a nice job on their forwards," Colorado defender Jeff Larentowicz said. "Our back forward didn't allow them too many opportunities."
Goalkeeper Nick Rimando made two saves for Real Salt Lake.
Real Salt Lake leads FC Dallas by three points in the West.
"Now our fate is in our own hands," Real Salt Lake coach Jason Kreis said. "Had we not picked up a point here, we would have been relying on Dallas to drop a result because they would have been in the driver's seat."
"At this point, we are in the driver's seat," Kreis said. "We pick up three points next week and we don't have to look around at anyone else or wild card. It's all in our hands."
The Rapids had the better of the scoring chances in the first half.
Wells Thompson missed an open net in the fourth minute and Rimando stopped Thompson with a diving save in the 45th minute.
Real Salt Lake defender Robbie Russell picked a loose ball inside the box, but his shot in the eighth minute sailed over the crossbar.
Larentowicz got behind the defense and Sanna Nyassi set him up with a cross. But Larentowicz's header in the 56th minute brushed the upper crossbar and ended up in the stands.
"I reacted late on the shot and hit it over the bar," Larentowicz said. "I reacted late and got under it."
Real Salt Lake came close to scoring in the 67th minute. Javier Morales missed the left post on a cross.
Caleb Folan missed the left post from 25 yards in the 82nd minute.
"Our objective was to get a shutout and to get a point and we did a pretty good job of it," Rimando said. "They threw everything at us at the end, but we battled and fought and we kept the shutout."