Keane had an assist and Sean Franklin set up two goals by the defending champion Galaxy, who will head to Seattle next Sunday in prime position to earn their third MLS Cup appearance in four years.
Michael Gspurning made three saves to avoid an even more disastrous result for the Sounders, who must beat the Galaxy by four goals next weekend to advance to the franchise's first MLS Cup final.
If Los Angeles survives and Houston wraps up the Eastern Conference finals after beating D.C. United 3-1 earlier Sunday, the MLS Cup would be a rematch of last season's game, when David Beckham and the Galaxy won it all at Home Depot Center.
The Galaxy entered the postseason as the West's fourth seed but have maintained the impressive form they showed down the regular-season stretch. After beating Vancouver in a knockout playoff and ousting Supporters' Shield-winning San Jose in the first round, Los Angeles largely dominated the talented Sounders particularly while scoring two goals in three minutes early in the second half.
Keane converted a header on a pass from Landon Donovan in first-half injury time before tapping home his fourth goal of a dynamite postseason in the 67th minute.
Keane has been brilliant in his first full MLS season despite spending much of the year on planes for international duty as Ireland's captain at Euro 2012 and elsewhere. He also scored two goals in the second leg of the first round at San Jose, leading the Galaxy back from a first-leg deficit.
Magee scored the prettiest goal in a half full of a brilliant passing by the Galaxy in the 64th, with Beckham and Keane finding Franklin to set up Magee's third goal in Los Angeles' four playoff games.
Neither team had much trouble getting started on a chilly night south of Hollywood. The Galaxy had most of the scoring chances in the first half, but Seattle's Austrian goalie was sharp, catching Donovan's header on the fly midway through the first half.
Los Angeles finally connected in the only minute of injury time on a play begun by Franklin, who came down the wing and centered it for Christian Wilhelmsson and Donovan, who chased it nearly to the end line before popping it in front. Keane backpedaled, yet still had the body control and strength to head it past the sliding Gspurning.
Keane did his trademark cartwheel-somersault goal celebration in front of the L.A. Riot Squad and turned to catch Donovan, who leaped into his arms.
The Galaxy were far superior after halftime, and a dazzling sequence of passing ended with an emphatic goal by Magee, who has scored in six of Los Angeles' last eight playoff games dating to last season.
Three minutes later, Keane pounced on a loose ball in front of Gspurning's net after Wilhelmsson's efforts, tapping it home to start the rout.