Sean Franklin's brace put the Galaxy in a good position, but LA could not close the deal against a resolute Sporting Kansas City side in a dramatic finish.
Sean Franklin gave Los Angeles the lead twice, only for Kansas City to pull back both times, first through Julio Cesar and then with a 92nd minute Omar Bravo penalty. Kansas City will feel further hard done as they had a goal from Aurelien Collin chalked off for a very tight offside call.
Both sides applied early pressure without results in the early minutes, though Graham Zusi's dipping shot went just over the bar in the 15th minute for the best chance of the early stages.
However, the Galaxy ended up taking the lead in the 24th minute as a looping header from Omar Gonzalez found the foot of Franklin, who converted coolly. There were claims of offside from Kansas City, but replays showed Collin clearly kept Franklin onside.
The home team pressed hard for the equaliser, though another effort over the bar from Zusi was the best they could muster. The Galaxy, meanwhile, looked dangerous on the counter, and Adam Cristman was nearly through on goal after a fine pass from David Beckham, only to be held back by the offside flag.
The Galaxy pressed in the opening minutes of the second half and Chad Barrett had an early attempt saved by Nielsen after the Sporting defense failed to clear out of the area. After the initial pressure, Kansas City started to push forward in search of an equaliser, but was hurt by a lack of creativity.
However, the home side finally got their leveller, but it wouldn't last for long. In the 72nd minute, Graham Zusi swung a corner to the back post, and it took a fortunate bounce before falling to Julio Cesar, who lashed home a volley.
The Galaxy retook the lead within minutes, though, as a poor clearance found David Beckham just outside the area. The English midfielder slotted through for Franklin, who calmly finished past Nielsen for his second of the game.
Just moments after a gaffe from Omar Gonzalez nearly gifted substitute Davy Arnaud a goal, Sporting thought they had retored partity as Collin rose up to head in from a free kick, but the linesman ruled his effort out for a very close offside position.
The disallowed goal was controversial, but Kansas City got a break in the 90th minute when Frankie Hejduk was whistled for controlling the ball with his hand in the box. Bravo stepped up and coolly converted the penalty to give his team a 92nd minute equaliser and a share of the points.