The Galaxy, which already had clinched its place in the knockout round, improved to 10 points atop Group 5 and will face Herediano of Costa Rica in March.
Nicolas Munoz scored twice, finishing the Group Stage with all six of his team's goals and the Champions League scoring lead.
Already assured of advancing and with a Sunday clash against the Seattle Sounders that could determine MLS playoff seeding pending, Los Angeles fielded what was essentially a reserve team. But the visitors pressured the host immediately had had two quality chances inside the first three minutes.
However both McBean and Pat Noonan were unable to get clean strikes inside of 10 meters.
Noonan again found space inside the box in the 15th minute, but his near-post header from eight meters was saved by Fidel Mondragon.
Finally, the Galaxy jumped in front when McBean snapped a header that stuck the underside of the crossbar and bounced just inside the line in the 38th minute.
Suarez came close to equalizing four minutes later, but he put his attempt off the crossbar.
Los Angeles thought it had a second goal just before halftime when Mondragon saved Rafael Garcia's low free kick from 26 meters. Stephens pounced on the rebound, but the assistant referee ruled that Mondragon had control of the ball before the 23-year-old American midfielder kicked it into the net.
McBean had another scoring chance in the 53rd, but Mondragon made a diving save on the 19-meter shot.
Two minutes later, Munoz scored the first of his two on the night, taking a cross from Paolo Suarez at the penalty spot and putting a shot that took a slight deflection past sliding LA goalkeeper Brian Perk to equalize.
Los Angeles took a 2-1 lead in the 62nd minute as Marcelo Sarvas chipped a free kick into the box where it was headed across the goal by Bryan Gaul. Noonan missed the ball, but McBean did not, hammering in his second from just inside the six-yard box.
Five minutes later though, Munoz equalized as he drove a free kick from the outside left edge of the box.
Just when it looked like the game was destined for a draw, Stephens struck, pouncing on a cross by Noonan that knocked off the post and pushing it into the net for his second CONCACAF Champions League goal.
The victory finished Los Angeles with the fourth-best record in the Group Stage, earning it the quarterfinal matchup with No. 5 Herediano.