A penalty from Cucho Hernandez and goal from Yaw Yeboah gave the Crew a 2-0 lead at the interval before Denis Bouanga pulled a goal back for LAFC in the 74th minute.
In what may have been the final game before retirement for former Italy captain Giorgio Chiellini and possibly a last appearance for LAFC for Mexican star Carlos Vela, last year's champions were convincingly beaten.
Columbus, coached by little-known Frenchman Wilfried Nancy, dominated the game for long stretches while Steve Cherundolo's LAFC were unable to unleash their trademark counter-attacks.
After a frantic start, in front of a loud, capacity 20,802 home crowd, Columbus quickly settled into their possession game thanks to the calming influence of veteran midfielder Darlington Nagbe.
French defender Steven Moreira had the first real opening, in the 16th minute, but his disappointing header from a promising position in the box was off target. The Crew's roaming Colombian striker Hernandez sent a reminder of his goal threat with a shot from 20 yards out which flashed wide of the post.
Uruguayan attacking midfielder Diego Rossi was increasingly influential as he began to find spaces behind Hernandez and he went close in the 27th minute with a shot into the side-netting.
The pressure on the Los Angeles defence was building but when the Crew broke through it was via a sightly fortunate penalty award. Yaw Yeboah crossed from the left, Rossi flicked the ball up in the air and it struck the shoulder of Diego Palacios and then his arm.
Referee Armando Villarreal had no hesitation pointing to the spot and Hernandez buried the penalty into the bottom corner to make it 1-0 in the 33rd minute. Within four minutes the Crew doubled their lead with a goal of perfect
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