LAFC midfielder Eduard Atuesta put the game away with a goal off a direct free kick in the 82nd minute when he curled a shot from just outside the corner of the penalty area into the right side of goal.
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LAFC (20-4-8, 68 points) finally clinched the best record in the league, in just its second season, by ending a five-match winless streak. The team did have four ties during that stretch but had not won since Aug. 21 against San Jose.
Vela became just the second player in MLS history to score 30 goals in a season as he moved one away from the record set by Atlanta United's Josef Martinez last season. Vela became the first player in league history with 30 goals and 15 assists in the same season.
LAFC seemed doomed to another tie, which would have left them just short of clinching the Supporters' Shield. But Rossi scored an opportunistic goal late in the second half off a diving header.
Dynamo defender Maynor Figueroa tried to clear a ball out of the Houston penalty area, but the ball hit off the crossbar and came back onto the field. Rossi went with a diving header off a high bounce and beat Dynamo goalkeeper Joe Willis for his 16th of the season.
Vela scored a goal in his seventh consecutive game when he converted on a penalty kick in the 23rd minute for a 1-0 lead. Lee Nguyen earned the attempt when he was fouled in the penalty area by Houston's Kiki Struna.
The Dynamo (11-17-4, 37 points) tied the score 1-1 in the 28th minute on an LAFC own goal. Struna directed a loose ball in the LAFC penalty area toward goal. The ball was cleared off the line by LAFC's Mohamed El-Munir, but it rebounded off goalkeeper Tyler Miller and into the net.
With two games to play in the regular season, LAFC are now three points behind the New York Red Bulls' MLS record of 71 points in a season set last year.
LAFC clinch Supporters' Shield in win vs. Houston
LAFC laid claim to the best regular season record in MLS following their 3-1 victory over the Houston Dynamo. For more MLS, sign up for ESPN+.