The Sounders took a 1-0 lead on an own-goal by Portland's Mamadou Danso in the 25th minute, and Johnson doubled the advantage 3 minutes later when he chipped home a cross from Brad Evans.
Montero added an insurance tally in the second half, putting in his own rebound after his first shot was stopped by Timbers goalkeeper Donovan Ricketts in the 62nd.
Seattle (14-7-10, 52 points) vaulted over the Los Angeles Galaxy into sole possession of third place in the Western Conference with three games to play.
Portland fell to 7-16-9.
Celebrity Families of 2014 [PHOTOS]