Portland played a man short during the entire second half, making it easy for Salt Lake to increase its lead in the Western Conference.
Salt Lake (14-8-6) won for the third time in five matches and boosted its advantage over Los Angeles to eight points.
Portland was already facing a 2-1 deficit when Ben Zemanski was sent off at the end of the first half with a direct red card.
Plata scored in the 15th minute to give Salt Lake a 2-0 lead. He assisted on a goal by Luis Gill in the ninth minute and Javier Morales shortly after halftime.
Portland (9-5-12) has earned just one point in its last seven games and is in fourth place in the West.