The Kings will try to stay unbeaten in regulation under Sutter on Thursday night when they meet the Winnipeg Jets, who have emerged as one of the Eastern Conference's best home teams.
Los Angeles improved to 3-0-1 since Sutter took over for the fired Terry Murray earlier this month following Wednesday's impressive 2-0 win at league-leading Chicago.
Quick made 38 saves for his NHL-leading fifth shutout while Trent Hunter and Jarret Stoll scored.
"That took four lines, six 'D' and a goalie. That was a big effort by everybody," said Quick, who's allowed eight goals as Los Angeles has posted a 4-0-1 record in its last five overall.
Quick has fared poorly when facing the Jets franchise, though, going 1-1-0 with a 4.13 goals-against average in three career starts.
The Kings killed off all four Chicago power-play opportunities, running their streak to 20 in a row. Los Angeles has killed off 65 of its last 68 short-handed situations stretching back to Nov. 22.
"We've been doing a real good effort on the PK the last couple of weeks here. ... Guys are competing, guys are battling," Quick said. "We expect ourselves to be doing something like that."
Wednesday's contest marked the 15th time in 16 games that the Kings (18-14-5) have been held to two goals or fewer, though they have gone 7-7-2 over that stretch and are just one point behind San Jose for the Pacific Division lead.
Los Angeles, which ranks last in the NHL with an average of 2.14 goals per game, may find scoring even tougher Thursday without Simon Gagne, who will miss his second straight game due to a concussion. Gagne is fourth on the club with seven goals, including two game-winners.
The Kings will face a Jets team that's tied with Washington for the second-most home wins by an Eastern Conference team with 12. Winnipeg (17-14-5) has been inconsistent lately, though, having alternated wins and losses in its last eight games including Tuesday's 4-1 victory at Colorado.
Evander Kane scored twice to snap a seven-game personal goal drought as the Jets won for just the fifth time in 17 road games this season.
"It was a big win for us. It was on the road, and we need to improve our road record," Kane said. "In a lot of facets we rose to the occasion."
Kane already has a team-best 17 goals in 35 games - two short of matching his career high set in 73 games last season while the team was still in Atlanta. However, he's failed to score in his last six games at the MTS Centre.
Ondrej Pavelec, who stopped 32 shots in the win over the Avalanche, blanked the Kings in his only appearance against them. He turned aside 38 shots and was helped by two goals from Kane as Atlanta won 7-0 on Nov. 13, 2009.
The Jets franchise has won three straight against Los Angeles by a 17-5 margin.