Second-half goals from Sebastian Lletget and Jonathan dos Santos saw the Galaxy past hosts Minnesota in the first round of the play-offs on Sunday.
After a scoreless first half at Allianz Field, Zlatan Ibrahimovic's Galaxy broke the deadlock via Lletget – who bounced on a deflected shot by the former Manchester United striker with 19 minutes remaining.
Dos Santos doubled the lead four minutes later with a curling effort beyond Minnesota goalkeeper and ex-Arsenal shot-stopper Vito Mannone.
Jan Gregus scored a late goal for Minnesota, but the Galaxy were not to be denied as they look ahead to a mouth-watering clash against Supporters' Shield champions LAFC.
In Sunday's other play-off match, Philadelphia Union prevailed 4-3 against New York Red Bulls after extra time in an historic victory.
The Union overcame the Red Bulls in a thriller for their first play-off victory, having lost their four previous post-season matches.
Philadelphia trailed 2-0 and 3-1 but rallied on both occasions to force extra time as Marco Fabian's 106th-minute goal sent the Union through to the next round.
Next up for the Union are defending champions Atlanta United in the Eastern Conference semis.