The blowout win gave the Galaxy's playoff hopes a boost and effectively put an end to any postseason aspirations for SKC also saw Ibrahimovic take over the record for most goals in a single season by a Galaxy player with 26. That's more than half of his team's 49 total goals.
The Galaxy, which trailed 1-0 before exploding for seven unanswered goals, shot upward from eighth place in Major League Soccer's Western Conference to fifth at the end of a weekend that saw the three teams in front of the Galaxy lose their respective matches.
Los Angeles (14-13-3) put an end to a four-match winless streak. They also might have stopped Sporting KC's streak of eight straight seasons in the MLS playoffs.
SKC (10-13-7) is six points out of a playoff spot -- the top seven in the East and West get in -- with only four games left to play in the regular season.
The Galaxy drew even after a handball in the box in the 30th minute. Ibrahimovic's penalty kick was initially saved by Sporting KC goalkeeper Tim Melia, but Ibrahimovic was the first one to the rebound, and he put it in to tie the score at 1.
Both teams had plenty of chances to break the tie until Joe Corona's header in the 48th minute. It was Corona's first goal of the season.
Ibrahimovic left-footed a shot from close range past Melia for a 3-1 lead in the 51st minute, and Uriel Antuna tallied in the 69th minute, his fourth of the season.
Rolf Feltscher had two assists for the Galaxy after Felipe Gutierrez opened the scoring with Sporting Kansas City's first goal of the match, in the 24th minute. Gutierrez added his second in the 86th minute.
Lletget scored his two goals two minutes apart, with the Galaxy ahead 4-1 and well in control. He has three on the season.
Gutierrez scored the game's final goal, but Ibrahimovic capped off the night in the 85th minute for Galaxy fans with a long strike from the wing just inside the box, then held aloft three fingers and stood on a sign board with his arms raised to the crowd.