Khudobin made 30 saves for the Stars (12-10-3), who have lost four of five (1-3-1).
Connor McDavid came close to scoring at 1:12 of overtime, but his attempt on a breakaway was swept off the goal line by Stars defenseman Gavin Bayreuther. The play was reviewed, and it was determined the puck did not completely cross the goal line.
"Our focal point was keeping an eye on Connor McDavid and he got a breakaway," Bayreuther said. "You have to retreat back to the house no matter what, and luckily, I knew it didn't go in, but it was close. Unfortunately, they scored shortly after."
Dallas had an excellent opportunity to win the game when the puck bounced to Jamie Benn in the slot with three seconds left in the third period. Benn had Tyler Seguin open at the side of the net but elected to shoot, and Koskinen made the save as time expired.
"When your best players have the puck on their sticks, you trust their instincts," Stars coach Jim Montgomery said. "Jamie thought he found a hole, and I'm not sure if he knew [Seguin] was on the back door or not. Usually he makes that play, but I think he saw a hole there to try and finish the game."