Colorado (8-14-1) had been outscored 11-4 during the skid. The Rapids hadn't collected a point since a 3-0 win over the Portland Timbers on June 30.
Pickens made one save as he posted his sixth shutout of the year and 38th of his career in gaining his 40th win with Colorado. He had been tied at 39 with Marcus Hahnemann.
Rapids midfielder Brian Mullan became the 15th player to appear in 300 MLS games.
Nane scored on a rebound after the Rapids had pressured Real Salt Lake goalkeeper Nick Rimando.
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