"We did simple things. We got pucks to the net and we didn't take penalties. We did all the little things," Stars coach Glen Gulutzan said.
Derek Roy had a goal and two assists, Erik Cole scored his first goal for Dallas since a trade with the Montreal Canadiens on Tuesday, and Loui Eriksson and Jaromir Jagr provided insurance in the third period.
"Yesterday was the first time he [Roy] said he felt completely healthy," Gulutzan said. "He was quick on pucks. He was making plays. You can't give him space because he can find the guy. I thought he was real good tonight, a big catalyst for us, and that's what we're going to get moving forward. "
Stars goalie Kari Lehtonen delivered a 25-save performance for his eighth victory of the season, and Dallas ended a two-game losing streak three days after suffering a 5-1 home loss to the Edmonton Oilers.
"He [Lehtonen] didn't have to hang on a tightrope and he shouldn't have to. I thought he was solid and gave us a shot to win," Gulutzan said.
But early on it looked like this game might be a repeat of the previous meeting between the Stars and Blues, a game Jan. 26 in Dallas that ended in a 4-3 win for St. Louis. David Perron had two goals for St. Louis in that win.
And when Perron netted his seventh of the season 4:20 into this game, tucking the puck just inside the left post on a beautiful display of precise stickhandling and skating, it looked like this might be the Blues' day.
However, before the puck dropped after the goal, Dallas' Antoine Roussel and St. Louis' Chris Stewart dropped the gloves, a scrum that everyone in the Stars' room felt gave them a much-needed spark to turn the game in their favor.
"I think Roussel's fight gave us a lift," Roy said. "They were chipping everything in, they have big bodies and were working us down low and we tried to do the same on the other end, but they were doing a good job defending. But [Roussel's] fight gave us a boost, and after that, we got that goal by Cole and we took off after that."
The Stars scored four unanswered goals to send the Blues to defeat in the first game of a five-game road trip.
"We had too many average performances," Blues coach Ken Hitchcock said. "What can you say? Too many average performances doesn't get it done on the road."
St. Louis defenseman Kevin Shattenkirk summed up Sunday's loss, the Blues' third away from home this season, in basic terms.
"I think they just outbattled us for the most of the game," Shattenkirk said. "We weren't able to put pucks in the net. We had our opportunities there to bang some in. We just couldn't seem to get it by Lehtonen. We didn't draw too many penalties either. We feed off our power play and we weren't able to get that going either. It was a tough one all around."
Dallas tied it 1-1 at 15:49 of the first when Cole beat goaltender Brian Elliott with a 15-foot wrister from the slot. After two St. Louis turnovers in their end, Roy fed Roussel, who laid the puck back to Cole, who converted for the goal.
The Stars took the lead 2-1 with 1:40 remaining before the first intermission when Roy scored his third of the season. After T.J. Oshie turned over the puck along the right boards, Roy dashed in and flicked a 33-foot wrister that trickled under the right shoulder of Elliott, giving Dallas' revamped second line its second goal of the period.
An apparent game-tying goal by Blues rookie Adam Cracknell at 8:59 of the third was nullified when officials determined he used a kicking motion to score.
Eriksson's seventh of the season from the right face-off circle, which came after a cross-ice pass from Jordie Benn at 12:48, made it 3-1, and Jagr's seventh of the season with 1:00 remaining made it 4-1.
"When you score one goal, usually another goal comes next game and it was nice to get one today again," Eriksson said. "It was a nice pass from Jordie and it was nice to see that go in, and definitely to get the win."
Elliott stopped 23 of 27 shots in his first start since Feb. 11 to receive his sixth straight loss.
The teams return to the ice on the road at Los Angeles later this week. St. Louis will face the Kings at Staples Center on Tuesday, two days before Dallas meets the defending Stanley Cup champions for the first time this season.