Larkin's frustrations boiled over at the end of the second when he was cross-checked into the boards by Stars defenseman Esa Lindell. Larkin took exception to the hit and immediately dropped the gloves, taking Lindell to the ice as the horn sounded, and both players were assessed five-minute majors for fighting to start the third period.
With an extra attacker at 16:13 of the third, the Red Wings' captain relieved a bit of frustration when he fired a shot from the left slot that beat Oettinger to make it a 4-2 game, but Blake Comeau earned an empty-net goal with 53 seconds remaining to put the game on ice.
Greiss made 11 saves and didn't allow a goal in nearly 24 minutes of action, but the Wings' comeback fell short for the second straight night as Detroit dropped its fifth game in six contests against Dallas this season.
The Red Wings hope to flip the script on the Stars as the four-game home-and-home series shifts to Little Caesars Arena to wrap up the clubs' season series on Thursday and Saturday.
Puck drop for Thursday's matchup is set for 7:30 p.m. with the TV broadcast on Bally Sports Detroit.