Lars Eller put a stop to Montreal's third-period meltdowns.
Eller scored the midway through the third period after Dallas scored twice to tie it, leading Canadiens to a 6-4 win over the Stars on Thursday night.
"It was just one of those crazy games," said Eller, who scored by putting a shot over Dallas goalie Kari Lehtonen's left shoulder to the short side. "Usually we don't score a lot of goals, but the last two games it seems like the puck is going in more."
Max Pacioretty added an empty-netter in the closing minutes as the Canadiens finished their longest road trip of the season at 3-2-1.
On Tuesday night at Carolina, the Canadiens led 3-0 going into the third-period but lost 5-4 in overtime.
"It's a big win, but I've got to look at the road trip," Montreal coach Michel Therrien said. "We had a chance to make a good road trip, and this is exactly what we did.
"This (Dallas) is a good hockey team, and they were playing well lately," he added, "so it was a good challenge for us."
Pacioretty had two goals, giving him a team-high of 19, and two assists. P.K. Subban had a goal and three assists. Brendan Gallagher and David Desharnais also scored for Montreal (24-14-4).
Valeri Nichushkin converted a penalty shot for Dallas. Jamie Benn, Tyler Seguin and Brenden Dillon also tallied for the Stars (20-13-7).
Dallas lost in regulation for the first time in eight games, ending its longest streak of games with a point this season at 5-0-2.
"I was concerned after going through the stretch we went through with a couple real emotional wins that we might get loose, and we were loose," Stars coach Lindy Ruff said. "Parts of this game, I thought we gambled on the offensive side and gave up some real good chances that we normally don't give up."
Seguin, whose goal and assist gave him club highs with 21 goals and 41 points, said the Stars didn't deserve to win.
"I think we got a little complacent after having a soft few games in a row," he said. "We gave `em a lot, gave `em a lot of opportunities. Our goalie made some unbelievable saves. (We) kind of left him hangin' out to dry, including myself."
Seguin scored at 7:42 of the third period on the power play and Dillon followed 47 seconds later to tie the score at 4.
Subban called them lucky goals.
"Don't get me wrong; they worked hard and they created opportunities for themselves," Subban said. "But two knuckle pucks, and they're very deceiving or fortunate."
Then Eller netted his 10th of the season at10:39 to put Montreal ahead for good.
Nichushkin, taken down by Canadiens defenseman Josh Gorges near the crease, beat goalie Carey Price to his glove side on the penalty shot to tie the score at 2-2 early in the second period.
Subban scored at 6:30 to put Montreal ahead. Price got his second assist of the season on the goal.
Subban earlier made a backhand pass while wheeling through the left circle to set up Desharnais in the slot for a shot that beat Lehtonen, who was screened and falling in the crease, to give Montreal a 2-1 lead.
Benn opened the scoring with his 14th goal of the season at 6:12 of the first period. He struck a one-timer near the right point following a cross-ice pass out of the left corner from Seguin.
That extended Benn's streak of consecutive games with a point to five, including goals in four.
The Canadiens tied the score at the 11-minute mark of the period. Pacioretty took an outlet pass at the red line from Subban, raced in alone on the Dallas net and scored to Lehtonen's glove side.
NOTES: Montreal wing George Parros, sidelined since Dec. 14 with his second concussion of the season, left the team on Thursday morning and went to the University of Michigan to seek an opinion of a concussion specialist. ... Canadiens center Daniel Briere, the 36-year-old former All-Star, was a healthy scratch for the second straight game.