In the 67th minute, Montero took a feed from Brad Evans and pushed it past goalkeeper Bill Gaudette, who was making his debut after being acquired from the Los Angeles Galaxy on Friday.
Alvaro Fernandez scored in the 16th minute to give Seattle (8-5-7) a 1-0 lead. Adam Johansson made a perfect crossing pass from 45 yards out to a sliding Fernandez, who pushed the ball past Gaudette. Johansson's left-footed cross from the right sideline went over the head of Red Bulls defender Brandon Barklage directly to Fernandez's right foot.
Sebastien Le Toux, also making his debut with the Red Bulls after coming over in a trade Friday with Vancouver, tied the game in the 24th minute. Kenny Cooper blasted a shot from just outside the penalty area that Seattle goalie Bryan Meredith stopped, but Le Toux alertly followed and kicked it home.
Joel Lindpere gave the Red Bulls (9-5-5) a brief lead in in the 61st minute with his third goal of the season. Lindpere took a feed from Barklage, then faked out former Red Bulls defender Jeff Parke to unleash a left-footed blast from 25 yards out.
The Red Bulls remained unbeaten at home at 5-0-3.
Gaudette got the start in goal when rookie Ryan Meara was unable to go because of a hip injury.
Red Bulls defender Rafa Marquez left the game in the 21st minute with a left calf injury.
Marquez has played in just eight of the Red Bulls' 19 games this season because of suspensions or injuries. Signed to a multimillion-dollar contract in 2010, he has not scored a goal and has only two assists this season.