Chelsea struck first in the 34th minute, as Neto received a perfect downfield pass from Nicolas Jackson before sending defender Ryan Hollingshead to the ground with a fake and finding the back of the net with a strike that beat goalkeeper Hugo Lloris.
The all-important insurance goal in Monday's Group D match came in the 79th minute as Liam Delap sent in a beautiful cross to Fernandez, who finished with a left-footed shot from a few yards out.
Chelsea will continue its group play on Friday when it faces Flamengo in Philadelphia, while LAFC will play ES Tunis later that day in Nashville.
After a first half that saw Chelsea pick up a pair of yellow cards, the two sides had to be separated as Neto and Denis Bouanga clashed.
Chelsea nearly doubled its advantage in the 54th minute, when Neto's entry pass to Jackson in the box was headed toward the goal before Timothy Tillman blocked the attempt.
Bouanga had a great chance to even the score in the 57th minute, but the shot from the left of the box was saved by Robert Sanchez.
Manager Enzo Maresca was pleased with Chelsea's performance but was already looking towards the next match.
"Very good result. At this stage of the season it is also normal that you have to manage different kinds of things," he said.
"Overall the performance has been good.
"We have to recover. We have a game in three days so we will see.
"We are going to prepare in the best way and for sure try to win."
Monday's match was played in front of just 22,137 fans in the Mercedes-Benz Stadium that has a capacity of 71,000.
Chelsea played in front of more than 70,000 fans at the same venue against Newcastle in the Premier League's Summer Series just a couple of years ago but many seats were empty this time as Maresca's side claimed the first three points of their campaign.
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