Dwight King scored his third goal in two games and Quick tied a team record with his third career playoff shutout to give the Kings a dominating lead heading into Game 3 Thursday night in Los Angeles.
The Kings have won nine straight road playoff games in two seasons, matching the NHL record set by the New York Islanders from 1982-83.
Quick matched Felix Potvin's team record for playoff shutouts and Carter finished off his first career playoff hat trick in the third period, securing the Kings' seventh straight win overall.
The Coyotes played better early and fell apart late, becoming frustrated after being unable to contain the more-skilled Kings.
Phoenix was hit with a string of penalties starting late in the second period, including a game misconduct to captain Shane Doan for boarding Kings center Trevor Lewis. Martin Hanzal also received one for boarding Dustin Brown in the third period and the Coyotes had 13 penalties for 56 minutes - most coming after the final 5 minutes of the second period.
The Kings won the opener, 4-2, by outplaying and outhustling Phoenix.
Even with all of Phoenix's hard work early in Game 2 and a couple of line changes by coach Dave Tippett, the Kings still managed to score first. King got it, redirecting a shot by Drew Doughty that beat Mike Smith stick side late in the period.
Hard work in the corners by Mike Richards set up Los Angeles' second goal, by Carter. He muscled the puck past Smith's glove side as he was going down on a feed from Dustin Penner that made it 2-0 early in the second period.
Then things completely unraveled for the Coyotes.
Doan, who was suspended three games for elbowing earlier in the season, was given a game misconduct and a 5-minute boarding penalty for ramming Lewis from behind. Defenseman Keith Yandle was already in the penalty box and Daymond Langkow joined him after a slashing penalty, giving Los Angeles a two-man advantage for more than 2 minutes.
Brown was sent off for diving on a slash by Smith, but that didn't bother the Kings. Carter scored his second a few seconds later on a redirect of a shot by Anze Kopitar, putting Los Angeles up 3-0.
"It's no secret we've been struggling a bit with the power play and to get some goals will give us confidence on it," Carter said. "We have some pretty skilled guys out there on the power play."