Leading 1-0 in the 52nd minute, the Sounders doubled the advantage when Montero picked up a loose ball and found the near post for his sixth goal of the season.
Caskey then collected the first tally of his career on a shot from 35 yards out, giving Seattle an insurmountable lead.
Rose added his first MLS goal in the 88th and Eddie Johnson scored early in the game for the Sounders (10-5-7), who used the big win to pull within seven points of the San Jose Earthquakes atop the Western Conference standings.
Los Angeles (10-11-3) saw its five-game undefeated streak snapped.
Swim Week Miami Beach 2014 [PHOTOS]