United (6-4-3) is undefeated in six home games after opening the season with a 1-0 loss to Kansas City.
Matt Pickens made eight saves for the Rapids (5-6-0). They went 1-2 on a three-game trip.
The Rapids, shut out for the third time this season, are 1-8-5 in Washington since 2000.
Salihi, signed as a designated player from Austrian club Rapid Vienna this winter, scored twice in United’s recent three-game trip.
After twice forcing saves from Pickens on close-range headers, Salihi got his first home goal in the 60th minute, sweeping in the rebound of Branko Boskovic’s header.
De Rosario put United ahead in the 25th minute when he reached Lewis Neal’s diagonal ball after Neal turned a midfield giveaway into a counterattack.
It was Neal’s first assist of the season, in just his second start.
Two minutes later, Pickens made two impressive saves to keep Colorado in it, pushing over De Rosario’s deflected shot before thwarting Robbie Russel’s header off Boskovic’s corner. Pickens also denied Salihi’s goal-bound effort, also from Boskovic’s corner kick, 2 minutes into the second half.
Bill Hamid needed just two saves to preserve United’s fourth shutout of the season. United will play twice more at home during the next 10 days, then won’t return until a June 30 game against Montreal.
The Rapids will play five of their next six games at home.
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