A penalty from Alvaro Saborio and Kyle Beckerman's strike saw Real triumph, taking them to 56 points, two ahead of fourth-placed FC Dallas with a game to play.
The top three teams in each conference will get a week off to begin the MLS play-offs and RSL can only miss out on that rest if Dallas defeat Portland Timbers on Saturday.
RSL hit the front in the 36th minute after Chivas defender Bobby Burling was judged to have pushed Saborio in the box and the Costa Rican striker made no mistake from the spot.
It went from bad to worse for the visitors in the 56th minute, Chivas midfielder Marvin Chavez was shown a straight red card for kicking the ball at an assistant referee, although replays suggested it was far from intentional.
Beckerman secured victory for the hosts with 16 minutes remaining with a sharp finish from inside the box.
If Real hold onto third position they will play either Seattle Sounders or Los Angeles Galaxy in the West's semi-finals.
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