Carter helped out on Mike Richard's tally just 1:38 into the game and then added his owner power-play goal later in the first period for a 2-0 Los Angeles lead.
Quick stopped nine shots in the first period while improving to 13-11-3 on the season for the Kings, who hold the fourth playoff seed in the Western Conference.
Slava Voynov and Drew Doughty each added a goal in the win.
Magnus Paajarvi scored and Devan Dubnyk made 35 saves for the Oilers, who remained three points out of a Western Conference post-season slot.
Interpol investigating stolen passports on missing flight
Senate Democrats to pull all-nighter on climate change