After the Oilers turned the puck over at the Kings' blue-line, Carter beat Oilers goalie Nikolai Khabibulin through the legs with a quick shot.
Los Angeles then put the game away with an empty-net goal by Jarret Stoll.
Sam Gagner replied for the Oilers (6-6-3), who have lost two of their last three, all at home. Khabibulin stopped 35 shots in taking the loss.
Edmonton had the best chances in the early running as Taylor Hall dropped a pass to Jordan Eberle three minutes in but he hit the post behind Quick. A minute later Quick, was forced to come up with a big toe save on another solid opportunity for Hall.
The Kings took a 1-0 lead at 4:44 of the second period when Khabibulin made a save on a long shot by Jordan Nolan but the Oilers were unable to clear the rebound as Fraser swooped in for his first of the season.
Los Angeles held the bulk of the momentum in the period, at one point outshooting Edmonton 13-1, but the Oilers fought back to tie things up.
Seconds after Khabibulin made a diving save after an odd bounce off the boards, Edmonton connected on the power play as a Gagner shot beat a screened Quick at 16:50.
Edmonton once again had a glorious chance denied three minutes into the third as Quick stoned Hall point blank on a shot from the top of the crease.
The Kings conclude a three-game road trip in Calgary on Wednesday. The Oilers play the fourth game of a five-game homestand on Thursday against Minnesota before heading out on a nine-game road swing.
Notes: It was the second of three games between the two teams this season. Edmonton won the first matchup on Jan. 24 in dramatic fashion as rookie Nail Yakupov scored with 4.7 seconds to send the game to overtime. Sam Gagner finished it off for a 2-1 Oilers at Rexall Place. ... Los Angeles came into the game having scored the fewest goals of any team this season with 30 in 13 games played. ... Khabibulin made just his second start in the Edmonton net this season after coming in to start the second and earning his first win in over a year in the Oilers' dramatic come-from-behind 6-4 win over the Colorado Avalanche on Saturday. ... Kings defencemen Alec Martinez (upper body) and Willie Mitchell (knee) remained out for L.A. and are day-to-day, while Matt Greene (back) is out indefinitely. ... Teemu Hartikainen was back in the lineup for the Oilers, while Lennart Petrell (head) and Ryan Jones (eye) are day-to-day. Anton Lander (foot) and Andy Sutton (knee) are out indefinitely. ... Former Oilers forward Dustin Penner played in just his seventh game of the season for the Kings.