Seguin matched his career high with four assists - on Dallas' first four goals - to help the Stars beat the
Though Seguin and Jamie Benn combined for seven assists, their line had only one goal, by Eaves to open the scoring at 6:35 of the second period.
''Probably their best game of the year,'' Stars coach Lindy Ruff said. ''Moved the puck well. Obviously, Tyler played a heck of a game with four assists, Jamie right behind him. Our best players were at the forefront tonight, which was great to see.''
To Seguin, the victory was especially significant because it was a Central Division game against the team that eliminated the Stars from the 2016 playoffs.
Seguin had scored three of Dallas' six goals in the previous five games. The Stars matched that total Thursday to end an 0-2-1 skid.
Eaves deflected a shot by Seguin for the first goal.
Seguin set up Jamie Benn for a breakaway, then gathered the rebound after Allen's save and passed out to Klingberg at the right faceoff dot for his first goal this season and a 2-1 lead.
''There's been a couple of chances,'' Klingberg said, ''and it's nice to see it finally go in there.''
Seguin passed to Stephen Johns for the first of four Dallas goals in the third period. The fourth assist came when Seguin's shot went in off teammate Jason Spezza.
''We're getting opportunities,'' Seguin said. ''They're going to go in. Eventually that's going to land in the right area, or it's going to go off a body.''
Stars defensemen combined for four goals.
''We've been trying to get our defensemen more involved,'' Ruff said, ''and I think overall they all were.''
''We're not playing very well,'' coach Ken Hitchcock said. ''We're not all on board where we should be and it's a tough time for us right now. We're going to have to build some momentum back with better play and more committed play. It's frustrating because we're not scoring and we're not keeping it out of our net the last two games.''
St. Louis tied the game 1-all on Stastny's goal at 11:26 of the second, but Klingberg scored 31 seconds later to give Dallas a lead it didn't lose.
Pietrangelo scored at 10:27 of the third. He and Stastny each had a goal and an assist.
NOTES: It was the first regular-season game between the teams since St. Louis beat Dallas 6-1 in the deciding Game 7 of their Western Conference semifinal last season. Play between the division rivals became chippy, with two fights in the second period and coincidental minor penalties for roughing in the third. ... St. Louis entered the game ranked 16th in the NHL in shots on goal per game, but 28th in goals per game. ... Seguin's previous four-assist game was on Oct. 18, 2014, against Philadelphia. He has seven points (three goals, four assists) in the last five games.
Blues: St. Louis will return home to face Columbus on Saturday.
Stars: They'll end a two-game homestand Saturday vs. Chicago.