Schmid returned to Los Angeles last month after replacing Curt Onalfo and his second spell at the helm is without a victory through three matches following Saturday's 2-0 loss at home to New York City FC.
Jonathan Lewis and NYCFC captain David Villa struck for the visitors as the Galaxy crashed to back-to-back defeats.
Lewis broke the deadlock with his first MLS goal, curling the ball up and over Galaxy goalkeeper Brian Rowe nine minutes into the second half.
Fresh from his match-winning hat-trick against the New York Red Bulls, Spain's all-time leading goalscorer Villa sealed the win in the 73rd minute with a stunning effort into the top corner of the net.
The Galaxy are ninth in the Western Conference – nine points outside of the playoff places – while NYCFC moved up to second in the east, leapfrogging the Fire following their 3-1 loss at the Columbus Crew.
Chicago surrendered a lead as the Fire dropped to third, albeit with a game in hand, and six points behind in-form leader Toronto.
Justin Morrow was at the double in Toronto's 4-1 drubbing of the visiting Portland Timbers.
After a goalless first half, Morrow scored twice after the break, while Victor Vazquez and Marco Delgado were also on target.
The Red Bulls came from behind to beat Orlando City 3-1, in a match that saw the visitors finish 10 men.
Kaka was sent off deep into stoppage time after a bizarre video review following a coming together of both teams.
As players were separated, Kaka jokingly put his hands on the face of former Orlando teammate Aurelien Collin amid plenty of smiles.
But MLS' new video replay system was called upon and Kaka was sensationally shown a red card, after referee Jorge Gonzalez issued cautions to Cristian Higuita and Sean Davis.
Clint Dempsey scored his 50th Seattle Sounders goal in a 1-0 win over Sporting Kansas City, the Montreal Impact eased past the Philadelphia Union 3-0, the Houston Dynamo trumped the San Jose Earthquakes by the same scoreline, the New England Revolution edged the Vancouver Whitecaps 1-0 and FC Dallas drew 0-0 with the Colorado Rapids.