The Stars, ranked No. 11 on the power play, were unable to score despite having a two-man advantage for 1:25 early in the first period. Dallas also failed to score with a two-man advantage for 1:19 midway through the third period.
"It was a key time in the game," Boucher said. "You've got to find ways to get goals."
St. Louis moved ahead 2-0 on Weight's power-play goal at 2:07 of the second period. Boyes made a pass across the crease that Weight tapped in from the right side.
"It was a big goal," Weight said. "We want to come out and make some plays. It's a part of this league. You've got to be at our best if you want to win."
Dallas cut the lead to 2-1 on Modano's score 5:55 into the second period. His 498th career goal came on a shot from the slot that caromed in off the left post in the second period.
St. Louis regained the two-goal lead when Stempniak scored with just under two minutes left in the middle period. It was his 10th point in the last 10 games.
Lehtinen scored on a wrist shot from the top of the right circle 3:29 into the third period to cut St. Louis' lead to 3-2.
"The third period was probably our best of the three," Modano said. "If we had started like that it might have been a different story."
The Blues went ahead 4-2 at 16:22 of the third when Boyes knocked in a loose puck. Petr Cajanek's shot hit Dallas goalie Mike Smith in the shoulder and Boyes tapped in the rebound.
Weight scored an empty-net goal with under two minutes to go. Weight has four goals and three assists in his last five games.
Dallas scored on a power play goal by Boucher with 12 seconds left. Dallas is 2-for-17 on the power play in its last four games.
Smith dropped to 4-2-1 in his last seven games in goal.
"He was just all right," Dallas coach Dave Tippett said of Smith.
St. Louis is 2-1-0 with Dallas this season. Both wins have come on home ice.
The Blues rank last in shots on goal at 26.8 a game. ... St. Louis forward Jamal Mayers skated in his 500th game. ... Dallas goalie Marty Turco, who was given the night off, is one win shy of his fourth consecutive 30-win season. Only Martin Brodeur has more consecutive 30-win seasons (11) among active goalies.
Copyright by STATS LLC and The Associated Press
Arena: Scottrade Center Location: Saint Louis, Missouri
Referees: Dennis LaRue, Ian Walsh Linesmen: Michel Cormier, Ryan Galloway
Attendance: 11,131 (58.1% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Eric Brewer (4)
Assists: David Backes, Jay McClement
Doug Weight (9)
(Power Play) Assists: Brad Boyes, Eric Brewer
Mike Modano (13)
Assists: Chris Conner, Loui Eriksson
Lee Stempniak (21)
Assists: Jay McClement, Jeff Woywitka
Jere Lehtinen (23)
Assists: Stu Barnes, Darryl Sydor
Brad Boyes (15)
Assists: Petr Cajanek, Matt Walker
Doug Weight (10)
(Empty Net) Assists: Jay McClement, Lee Stempniak
Philippe Boucher (18)
(Power Play) Assists: Mike Modano, Sergei Zubov