After a close first half in which Rossi scored his eighth MLS goal in the 21st minute, LAFC exploded for four goals in the second half. Bradley Wright-Phillips, Jose Cifuentes and Danny Musovski added goals for the home side.
LAFC ended a two-game losing streak, while San Jose lost for the second consecutive time, having fallen 3-2 loss to the Galaxy in Los Angeles on Saturday.
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Including a 4-1 loss to Minnesota in the MLS is Back Tournament quarterfinals -- a match that didn't count in the league standings -- San Jose has been outscored 12-4 in the last three games.
Danny Hoesen scored his first goal of the season just before the final whistle for San Jose, saving a little face on an otherwise forgettable night for his team.
LAFC continued its dominance over the Quakes in regular season play, winning the fifth of the five meetings between the two teams. LAFC has outscored San Jose 17-3 in those five games.
Wright-Phillips, a two-time Golden Boot winner in his eight-year MLS career, scored in the 49th minute, out-running Earthquakes rookie Tanner Beason and leapfrogging goalkeeper Daniel Vega for a toe-punch shot to give LAFC a two-goal lead.
Cifuentes and Musovski scored their first goals as LAFC players. Cifuentes made it 3-0 in the 64th minute, then Rossi struck again five minutes later for No. 9 on the season.
Musovski, a 72nd-minute substitute, scored in the 83rd minute. Wright-Phillips had six of LAFC's 19 shots to just eight as a team for San Jose.
Rossi scores brace in LAFC's 5-1 rout of San Jose
LAFC give the Quakes a night to forget with a 5-1 drubbing. Watch MLS on ESPN+.
Diego Rossi curls in LAFC's opener vs. San Jose
Major League Soccer: Diego Rossi (21') LAFC 1-0 San Jose Earthquakes. Watch MLS on ESPN+.