The result was Klingberg's fourth goal at 3:18 of overtime, lifting the Stars to a 3-2 victory over the Minnesota Wild on Saturday.
Klingberg got a cross-ice pass from Tyler Seguin and beat Devan Dubnyk, capping another solid night. Klingberg and Jamie Benn each had a goal and two assists for the Stars, who had all five shots on goal in overtime.
"I saw Jamie (Benn) bump the puck to (Seguin)," Klingberg said. "I was just trying to find an open lane for (Seguin) to find me there, and he was making a good saucer pass. It was pretty empty, and it was fun to see it go in."
Dallas' other two goals came on shots by the 23-year-old Klingberg that his teammates tipped in. He has 16 assists and 20 points, the most for any NHL defenseman.
"He was pretty darn good again," Stars coach Lindy Ruff said. "If he doesn't (score the goal), you might write a story about Dubnyk tonight. So now you get to write a story about John, which is well deserved."
Dubnyk finished with 33 saves, but he is 1-2 in the NHL's new 3-on-3 overtime.
"I'm starting to dislike it more and more as we go here," he said. "There should be a separate category for goals against."
It was another impressive victory for Dallas (14-4-0), which has won eight of 10 and leads the Central Division. Minnesota (10-3-3) had won three in a row.
"We battled back to get a point there after being down," Minnesota coach Mike Yeo said. "Three-on-3 certainly favors them. We just gave them too many odd-man rushes and obviously there's going to be some of that, but we got to make sure we're not giving up 2-on-1 after 2-on-1."
Kari Lehtonen made 22 saves for Dallas.
The Stars jumped in front one second after their first power play ended in the first. Spezza tipped the puck past Dubnyk for his first goal in 11 games.
"We've got a lot of games left against our division," Spezza said. "We feel like that's the reason we missed the playoffs last year, because we didn't win enough games in our division. It's no secret how good our division is."
The Wild tied it at 5:15 of the second period with a similar goal. Niederreiter tipped in Jared Spurgeon's drive from the blue line. The Stars challenged the goal because of possible goaltender interference, but the call was upheld.
It remained 1-1 after two periods.
Benn scored another tip-in goal on the power play at 2:26 of the third. Klingberg sent a slap shot from above the left faceoff circle, and Benn redirected the puck into the left side of the net.
Dallas held Minnesota without a shot on goal in the third period until 7:15, but it was Scandella's tying wrist shot from the top of the slot.
NOTES: Before the game, the Stars played the French national anthem in memory of the Paris shooting victims. Dallas LW Antoine Roussel is one of two current NHL players born in France, and his parents were in Paris on Friday. "That's the kind of thing the Stars do," Roussel said. "They're a class organization. The boys put some (French flag) stickers on their sticks. I really appreciate that from them." ... Spezza has seven of his 13 points this season at home (four goals, three assists). ... The Stars entered the game tied for the NHL lead with 3.65 goals per game. ... Dubnyk has a career record of 3-7-1 vs. Dallas.