John McCarthy finished with four saves to earn his fourth clean sheet of the season for the Galaxy (9-3-7).
Joveljic gave the Galaxy the lead for good when he scored unassisted in the 41st minute with a left-footed shot from the center of the box. It was his 11th goal of the season.
Joveljic added his fourth assist in the 49th minute when Fagúndez found the net for the third time this season.
Matt Freese saved three shots for New York City (9-7-2), which has lost two in a row after a five-match win streak.
NYCFC leads the all-time series 4-3-0 with a 2-3-0 mark in Carson.
The last time NYCFC came to town the Galaxy walked off with a 1-0 victory before a sellout crowd to kick off the 2022 season.
New York City stays on the road to play Nashville SC on Saturday. The Galaxy travel to play Real Salt Lake on Saturday.