Bouncing back against the Kings and getting back to their defensive mindset should make them feel much better.
"We needed to play well, not just because it was a big division game and they beat us last week, but we needed to get our game in order," Coyotes coach Dave Tippett said. "We still gave up 40 shots, but we competed the way we need to be successful."
Smith had a miserable game in California last Thursday, when he was pulled after allowing four goals on 15 shots in the first period of the Kings' 7-4 victory.
Both he and the Coyotes got off to a much better start in the rematch.
Phoenix was sharp early in its own zone and Smith was superb throughout, making numerous tough saves before Jarret Stoll beat him on a power play late in the third period.
The Coyotes broke open a tight game in the final 2 minutes of the second period on goals by Derek Morris and Shane Doan. Chipchura, who completed the Gordie Howe hat trick with a fight in the second period, scored his goal in the third, and Andy Miele had two assists for his first NHL points to help Phoenix improve to 5-0-1 at home.
"We talked about having a better start," Smith said. "Our start in LA the other day wasn't as close to being where it needed to against a good hockey team. I thought we did a good job tonight from the drop of the puck to respond to a tough loss in their building last time."
The Kings had won seven of their previous nine games and were sharp early, creating good chances while Ben Scrivens matched Smith nearly save for save.
The game fell apart for them late in the second period, when the Coyotes scored two goals against Scrivens on deflections and Smith kept making saves. Scrivens stopped 30 shots.
"They hadn't lost at home, so you knew you were going to need to make some saves in the first period and both goalies did," Kings coach Darryl Sutter said. "As the game went on, their goalie was on."
The Coyotes were trying to find a way to clean things up in their own end after a pair of wide-open games that featured 20 combined goals.
The latest was against Edmonton on Saturday, when Phoenix took a two-goal lead, lost it when the Oilers scored three straight and won 5-4 with a pair of third-period goals.
The one before that was the game in Los Angeles, where the Kings scored four goals in the first period, Phoenix rallied to tie it with four straight goals in 13 minutes and the Kings pulled away by scoring the final three, the last into an empty net to complete Dwight King's hat trick.
The rematch was more like these division rivals are used to playing, marked by solid defense, some big hits, along with plenty of testiness and trash talking.
The scoreless first period had plenty of action, featuring 20 minutes of penalties and five players in the box at one point.
The tension boiled over early in the second, when LA's Daniel Carcillo and Chipchura dropped the gloves for a fight near mid-ice.
Both teams traded good scoring chances in the period and both goalies were superb, turning away a combined 23 shots.
The Coyotes called a timeout after a flurry by the Kings late in the period and responded with two goals in the final 1:41.
Morris got the first on a shot from the point that caromed off Kings defenseman Robyn Regehr's skate and teammate Drew Doughty's leg. Doan followed with his 100th career power-play goal at 5.9 seconds, redirecting a shot by Oliver Ekman-Larsson from the point.
"It was tough, a couple tough bounces out there," Scrivens said. "But that's how you score goals in this league: Throw pucks to the net, get guys in front, get a fortuitous bounce. We've just got to take what we can from it and move on."
Chipchura put it all but out of reach in third period, when a cross by David Moss went off his skate past Scrivens. Smith gave up the power-play goal late in the game, but all that did was spoil the shutout, not the overall performance.
Martin Hanzal, Phoenix's second-leading scorer, served the first of a two-game suspension for charging Edmonton's Jeff Petry on Sunday. Forwards Jeff Halpern and Lauri Korpikoski, along with defenseman Rostislav Klesla, also were out with injuries. ... The Kings scored one goal or fewer for the third time in 13 games this season. ... Miele, called up before the game, had assists on the goals by Morris and Chipchura.