Pavelski, playing in his 1,248th game, became the 10th American-born player to reach the milestone when he tipped Miro Heiskanen's shot from the point.
“You kind of play it down as it’s happening because you really don’t want to think about it,” Pavelski said. “It takes you off your game a little bit. But when it went in, it was a good moment. You definitely feel that.”
Pavelski is a master at redirecting the puck for goals and reached the feat in typical fashion.
“What an appropriate goal to score for him,” Dallas coach Peter DeBoer said. “If you’re going to have a traditional Joe Pavelski goal, that’s what it would look like. It's appropriate that was his 1,000th point.”
The Stars, who have won four straight, tied idle Colorado for the Central Division lead with two games remaining.
“We’ve got to win the rest of our games in order to have a chance in our division and lock up home ice. We’ve got a lot to play for,” DeBoer said. “I’ve been on the other side of these situations. Those aren’t easy games for them but we came in and took care of business.”
Jason Robertson supplied a goal and two assists. Esa Lindell, Ty Dellandrea and Jamie Benn also scored for the Stars.
Dallas goaltenders Jake Oettinger and Scott Wedgewood combined for 19 saves.
David Perron scored for the Red Wings, who were playing their home finale.
Detroit's starting goaltender, Ville Husso, was replaced by Magnus Hellberg after giving up three goals in 12 minutes and 10 seconds.
Hintz tapped in his 36th goal through Husso's pads off a feed from Thomas Harley. Hintz's drop pass set up Lindell's shot from the point. Lindell's goal was his first in 18 games.
Max Domi's pass from behind the net led to Dellandrea's first goal in 23 games.
Robertson scored his 46th goal 55 seconds into the second period with a shot from the point during a power play.
Pavelski's goal at 3:37 of the period made it 5-0. His teammates spilled off the bench to congratulate him on the milestone.
“As soon as I saw it go in, I was turning to Miro and the boys were already on the ice,” Pavelski said. “It was pretty fun.”
Pavelski didn't have a point in the Stars' previous game against Vegas.
“He was sitting on 999 for one game. We were hoping to do it the last game but it was a great night to do it,” Benn said. “Just a typical Joe Pavelski goal. I don't think you could have drawn it up any better.”
Dallas led 6-1 when the period ended.
“We had them with two scoring chances in the first period and they scored three goals,” Detroit coach Derek Lalonde said. “That’s not entirely on our goalies, but it is hard to build much momentum in a situation like that. They had six goals on their seven scoring chances.”
Heiskanen, who had two assists, tied Sergei Lubov's franchise single-season record of 71 points by a defenseman. ... Robertson has 15 points in his last six games. ... Ottawa’s Claude Giroux also earned his 1,000th point on Monday, marking the first time in NHL history that two players reached 1,000 points in the same day. ... Detroit C Dylan Larkin recorded his 47th assist on Perron's goal, tying his career high.
Stars: Close out the regular season with a home-and-home set with St. Louis, beginning with a road game on Wednesday.
Red Wings: Visit Carolina on Tuesday.
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