LAFC scored a goal that counted 14 minutes later, as Cifuentes pounded home the rebound of a shot by Kim Moon-Hwan. Moon-Hwan took an entry pass from Eduard Atuesta and ripped a shot that Austin goalie Brad Stuver stopped. However, the ball bounced right to Cifuentes, who made short work of the opportunity.
It was the first time Austin FC trailed during the first four matches in its home stadium.
Rossi doubled the lead in the 89th minute, corralling a pass from Vela on a breakaway and steadying the ball once before beating Stuver to the bottom right corner.
Rookie goalkeeper Tomas Romero earned the third shutout of his four-match career for LAFC, recording four saves.
LAFC has won consecutive games for the first time this season and captured two games in a row on the road for the first time since beating the New England Revolution and Real Salt Lake in August 2019.
Austin was shut out for the eighth time this season. AFC have scored just 10 goals, nearly half of them in a 4-1 win against the Portland Timbers on Saturday.
Austin dominated the statistics, earning advantages in possession percentage (59.4 percent), total shots (14-12), total passes (502-345), passing accuracy (82.5 percent to 74.2 percent), corner kicks (8-3) and tackles won (14-10). Los Angeles had the edge in shots on goal (6-4), duels won (52-48), and clearances (12-5) ... and on the scoreboard.