The Stars have earned five points through three games of their five-game homestand.
"Just stay grounded," was the message Ruff gave to his team. "We have a lot of work ahead of us. Try to stay consistent. Our hard work ethic in the first 40 games has been good. If we can consistently work like that, then we'll have success."
"We easily could have won the last three," Kings coach Darryl Sutter said. "That's the way it goes."
The Kings, beaten at Chicago on Monday, will end a four-game trip on Thursday at St. Louis.
"You've got to work harder," Los Angeles defenseman Matt Greene said. "You've got to pay more attention to details and get back to playing our game. We're not playing as well as we can right now, and that's it.
"There's no moral victories. There's nothing like that going on here. Everybody has to raise their game to a level that they can play at and they've played at before."
Kari Lehtonen (16-8-7) stopped 23 shots for Dallas, which hasn't made the playoffs since 2008.
"Instead of winning a game and looking to see if we gained any ground, we decided to forget about that," said Cole, whose only other two-goal game this season was Saturday. "Just focus on our play and what we can do to win games.
"If we just focus on that, one day we'll wake up and we'll be in fifth or fourth or third or whatever."
Seguin reached 20 goals for the second time in his four-year NHL career. He had 29 goals in 2011-12 with Boston.
Dallas' previously anemic power play accounted for Cole's first goal and Seguin's tally. It was the first time the Stars have scored multiple power-play goals in a game since Oct. 11.
Dallas went into the game with the NHL's 29th-ranked power play (11.7 percent) and the league's worst at home (4.8 percent).
"I can't sit here and say that we weren't doing things properly before," Cole said. "We just weren't getting enough pucks at the net, and second and third chances, just (not) being as opportunistic as we should have been."
Seguin put Dallas ahead for good at 12:13 of the second period. He corralled a puck that caromed off the boards behind Ben Scrivens (17-5-4) and banged it off Scrivens' left skate as the goalie slid across the crease to try to cover the opposite post.
"That's how goal scorers score goals," Scrivens said. "They throw the puck. They find ways to score when it doesn't look like there's room. I've got to give credit to a good player, too."
Cole followed three minutes later with a wrist shot from a sharp angle near the goal line that beat Scrivens to his right.
Carter gave Los Angeles its first lead during a 4-on-3 power play with a deflection of Mike Richards' shot that popped over the right shoulder of Lehtonen and dribbled into the net.
About three minutes later, Cole tied it by swatting in a rebound that was nicked by Dallas' Alex Chiasson following a shot from the left point by Seguin 35 seconds into a power play.
Kopitar accounted for the final margin 1:05 into the third period with a shot from the left circle after Dallas' Benn brothers, Jamie and Jordie, got tangled up and lost the puck.
NOTES: Dallas forward Ray Whitney sat out with the flu, the first game that the 23-year NHL veteran has missed following 16 consecutive appearances. ... The Kings dropped to 4-2 in the second of back-to-back games. ... The Stars won the season series 2-1.
Copyright by STATS LLC and The Associated Press
DALLAS, TX - DECEMBER 31: Alex Goligoski #33 of the Dallas Stars handles the puck against the Los Angeles Kings...