Dallas snapped a four-game losing streak (0-3-1) and sent the Senators to their sixth consecutive defeat (0-5-1), tying Ottawa's longest skid this season.
Jordie Benn had two assists for the Stars. Cody Eakin had tied the game with a second-period goal. Kari Lehtonen made 26 saves in his second game since returning from a head injury sustained on March 11 in Dallas' previous victory.
Erik Karlsson netted Ottawa's goal in the first period.
Jamie Benn reached 30 goals for the first time in his five NHL seasons.
He took a pass from Tyler Seguin at the top of the left circle and fired a shot into the upper left corner of the net.
Leaner made 39 saves against Dallas, which had a 42-27 shots advantage.
Dallas outshot Ottawa 17-7 in the first period, but the Senators scored the only goal.
Dallas failed to score on three power plays in the second but the Stars broke through during 4-on-4 play with 4:53 left in the period.
Lehner stopped Valeri Nichushkin's attempt as he skated across the crease, but Eakin poked the rebound out from under the goalie to tie it.
NOTES: C Shawn Horcoff returned for Dallas after missing four games because of a broken finger. LW Erik Cole's streak of 269 consecutive games played ended because of an upper-body injury. He is day to day. . Despite their recent struggles, the Stars are 6-1-1 in their last eight home games. They are 5-1 in games in which defenseman Daley has scored. . Seguin extended his point streak to eight games (six goals, nine assists). . Ottawa defenseman Karlsson has points in six consecutive games (two goals, six assists). . In the teams' previous four games, they allowed 39 goals and 262 shots combined.