Greg McKegg, Adam Fox, Mika Zibanejad, Patrik Nemeth, Barclay Goodrow and Ryan Strome also scored for the Rangers, who have won four of six. K'Andre Miller and Dryden Hunt each had two assists and Igor Shesterkin stopped 30 shots.
Esa Lindell had a goal and an assist, and Tyler Seguin, Jason Robertson and Joe Pavelski also scored for Dallas, which has lost two straight after a four-game win streak. Roope Hintz and John Klingberg each had two assists and Jake Oettinger finished with 22 saves on 28 shots.
The Rangers spotted Dallas a two-goal lead less than five minutes into the game, then scored four times in a span of 5:05 for a 4-2 lead.
''They played hard and played the way we want to play,'' New York coach Gerard Gallant said. ''I was real happy with the response. This game didn't start out the way we wanted it to. We talked about it before the game, `Let's get back to playing our game.'''
The Rangers were coming off two losses by a combined score of 11-4 and then started slowly again Saturday.
''It was a little nerve-wracking there after the first two goals,'' Hunt said. ''The bench was pretty calm. I think guys just had enough of these terrible starts that we've had. We kind of left (Shesterkin) out to dry. To flip that switch, that was huge.''
McKegg, Fox and Zibanejad also scored in the first period. Zibanejad's goal came on the only power play of the first period. It lasted just 7 seconds before Panarin won the faceoff and Zibanejad blasted a slap shot off the left goalpost and past Oettinger.
''(The Rangers) like chaos,'' Dallas coach Rick Bowness said. ''We said that this morning - they're very creative on the rush. They've got a lot of speed and a lot of skill.''
Lindell got the Stars on the scoreboard 49 seconds into the game and then assisted on Seguin's tip-in goal at 4:53 for the early 2-0 lead.
''I was surprised,'' Lindell said of the shot that he flipped inside the near goalpost. ''I was just trying to get it to the net and get a rebound.''
Panarin's three assists gave him 51 for the season. He has 16 goals and leads the Rangers with 67 points.
Trailing 4-2 after 20 minutes, Dallas regrouped in the second period to put 13 shots on goal, including Robertson's eighth goal in the last five games on a power play.
Nemeth was awarded a goal after a video review showed that his shot from a scramble in front had crossed the goal line. That restored the Rangers' two-goal lead with 1:40 remaining in the middle period.
''There was some greasy goals around the front of the net,'' Gallant said. ''That's what we talked about. Play hard in the blue paint and do our job. We played a good, solid hockey game all around. I liked the way the team played. Everybody was involved.''
Pavelski's tip-in at 8:09 of the third pulled the Stars to 5-4. It was his 23rd of the season.
On a night with traffic in front of the net, each team scored twice on tip-ins.
''There was a lot of simple goals,'' Hunt said. ''Rebounds, tips, good use of going 5-hole. It wasn't anything pretty, just a lot of hard work and effort.''
Goodrow scored with 5:53 remaining and Strome's empty-netter with 1:37 left capped the scoring.
Oettinger allowed a career-high of six goals in his third season. Dallas was playing without veteran goalie Braden Holtby, out because of a lower-body injury. To back up Oettinger, the Stars recalled pro rookie Adam Scheel from Texas of the AHL.
When asked whether Oettinger would have been replaced if Holtby were available, Bowness said, ''It's a moot point.
''Jake's been better. He'll bounce back.''
NOTES: Panarin reached 50 assists for the fourth time in his seven NHL seasons. ... Seguin was playing in his 800th career game. ... Lindell's assist on the goal by Seguin was the 100th of the defenseman's career. ... The Rangers played with 11 forwards and seven defensemen, with RW Ryan Reaves sitting out. ''It was a coach's decision,'' Gallant said.
Rangers: Begin a two-game homestand on Tuesday against Anaheim.
Stars: Visit Toronto on Tuesday in the first of a four-game trip to begin a stretch of nine of 11 games on the road.
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