Bobby Boswell also had a goal for the United, which moved just two points behind the New England Revolution for the top spot in the Eastern Division in Major League Soccer.
Andy Williams scored the lone goal for Real Salt Lake, which has lost 10 in a row since beating Chivas, 2-1, back on Aug. 6. The 10-game losing streak is two shy of an MLS record.
Real Salt Lake has two games left in the regular season.
Each team had five shots on goal.
It was the second meeting ever between the two teams. Washington won the earlier meeting, 5-1.