Joel Lindpere had given New York a 2-1 lead 6 minutes earlier when he gathered in a pass from Brandon Barklage, beat Seattle defender Jeff Parke and fired a left-footed shot into the net.
But the Sounders (8-5-7) quickly responded as substitute Montero received a cross from Brad Evans and got a shot past New York goalkeeper Bill Gaudette.
Alvaro Fernandez also scored for Seattle, which extended its unbeaten streak to four games.
Sebastien Le Toux, acquired in a Friday trade, scored in his debut for the Red Bulls (9-5-5).
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