Phillip Danault gave the Kings a 1-0 lead at 3:58 of the first period, scoring from the slot after Trevor Moore's pass from behind the net missed Viktor Arvidsson near the left post.
Luke Glendening scored 43 seconds into the second period to tie it 1-1 when he received a pass in the left circle from Michael Raffl, who was falling down along the boards.
Kaliyev put the Kings back in front 2-1 at 8:54. He forced a turnover by John Klingberg in the defensive zone, skated down the right wing, and shot the puck off the far post.
Kaliyev made it 3-1 at 13:17 with a one-timer from the top of the right circle on the power play.
"The second period is what killed us in this game," Kaliyev said. "We sat back, made a lot of turnovers, and then we didn't get our forecheck. It cost us in the second period badly."
Jason Robertson cut it to 3-2 at 14:13, receiving a pass from Roope Hintz on a 2-on-1 and cutting around Drew Doughty in the slot before shooting glove side from low in the left circle.
"Even though we were down 3-1, we were really confident in the way we were playing," Stars coach Rick Bowness said. "We were controlling play and getting tons of chances. We just had to stay with the program. Play the right way, keep doing those things, and we got rewarded today."
Suter tied it 3-3 at 19:01 on a slap shot from the left point.
Alexander Radulov scored 46 seconds later on the power play to give Dallas a 4-3 lead. He beat Petersen from the edge of the crease after Suter's shot ricocheted to him off the end boards.
"I think the second period we were playing well, but we got a couple of bad breaks where they went and they scored, and we fall [down] by two goals," Radulov said. "We're a good team, and if we put up the good work, we're still going to be there. We get the one, the fans get pumped, and everybody on the bench was kind of going for it, and we get another one."
