Carter scored Los Angeles' first power-play goal of the season and added the only score in the shootout, leading the Kings to a 3-2 comeback victory over the Canucks on Monday night.
Voynov tied it with 43.2 seconds left in regulation for the defending NHL champions, who have won two straight after an 0-2-1 start. Jonathan Quick stopped 21 shots for the Kings, including all three Vancouver attempts in the shootout.
"Any time you get two points, you get a little boost of confidence, but it's only good for tonight," Quick said. "It's a playoff race right now, and every point is huge."
Until Voynov sneaked a long shot through traffic, the Kings were on the verge of adding another loss to their slow start since winning their franchise's first title. Los Angeles' impressive finish that recalled several big wins in last season's playoffs, including a couple against the Canucks in their stunning first-round series.
"We're still not the way we were in June last year, but we're getting there," said Anze Kopitar, who had an assist on Voynov's goal. "It's definitely a step in the right direction. We still have to work on things, and everyone in here thinks we can crank it up a notch. We just want to make sure we build on this win and roll ahead."
Luongo made 26 saves for Vancouver, which went 1-1-1 on a three-game California road trip. Zack Kassian scored his fourth goal of the season, and Alex Burrows also scored a slick wraparound goal as the Canucks nearly persevered to a grinding victory in their fourth game in six nights before narrowly allowing Voynov's goal, which eventually cost them a point.
"We emptied the tank," Vancouver coach Alain Vigneault said. "Our guys did what they had to do to have a chance against the Stanley Cup champions. When you get the type of effort like we did tonight, you feel like you should win. Losing is not fun, but at the end of the day, some of our guys took a step in the right direction. ... The puck had eyes (on Voynov's goal), because we were in the right areas, the right place."
Luongo was sharp in his second start since losing his job to Cory Schneider, and Los Angeles struggled offensively through 59 frustrating minutes until pulling Quick for an extra attacker. Voynov teed up a shot from the point that found a hole in heavy traffic, wobbling past Luongo for the Russian defenceman's first goal of the season.
After a scoreless overtime, Quick easily stopped Burrows, Alexander Edler and Kassian, while Carter beat Luongo in the third shootout round.
"It's a short year, and you want to bank as many points as you can," said Luongo, who got benched in favour of Schneider during last season's playoff series. "We were in control tonight, and it's disappointing."
The clubs hadn't met since the eighth-seeded Kings eliminated the Presidents' Trophy-winning Canucks in five games before romping through the next three rounds to the title.
Although Los Angeles handily won the clubs' playoff series last spring, a 111-point Vancouver team arguably gave the Kings their toughest test during their 16-4 rampage through the post-season. The Kings persevered through several tight games against Vancouver, capped by an overtime victory in the Game 5 clincher.
The Kings got blown out by Chicago in their banner-raising season opener before winning once on a three-game road trip. Los Angeles finally returned home to face the Canucks, who made their second appearance in Southern California already this season after routing Anaheim last week.
Vancouver already had a 2-0 lead when the Kings ended their 0-for-25 start on the power play this season.
Kassian scored late in the first period when Quick allowed a rebound of Edler's long shot from the point out of a faceoff, easily knocking home his fourth goal in six games to start the season. Burrows then came from behind the net early in the second period and sneaked the puck between the post and Quick's skate.
"That's my fault," Quick said. "He had it on his backhand, and as he pulled it to his forehand, he opened his blade a little, and I bit on the (possible) pass."
The Kings finally ended their man-advantage drought when Carter scored out of a faceoff just 7 seconds after Chris Tanev went off for high-sticking.
NOTES: Kings F Dustin Penner was a healthy scratch for the third straight game. Coach Darryl Sutter wasn't pleased with the two-time Stanley Cup champion's early efforts. ... Canucks C Manny Malhotra returned to the lineup after missing two games following the birth of his son. Andrew Ebbett was scratched. ... Kings captain Dustin Brown played in his 600th NHL game, all with Los Angeles ... The Kings welcomed their 25 millionth fan to Staples Center, presenting season tickets and a wealth of merchandise to 21-year-old Dustin Kramer of Torrance, Calif.