Evening up the score a little over four minutes later, the Stars got on the board when, after a faceoff win in the offensive zone, John Klingberg gathered the puck and fired a shot from the point that was then redicted by Michael Raffl past Sergei Bobrovsky and into the twine to make it a 1-1 contest at 12:53.
Despite heading into the first intermission tied, Florida led 13-7 in scoring chances.
Finding the back of the net once again - this time while on the penalty kill - Barkov regained the lead for the Panthers when he took a pass from Aaron Ekblad, finessed his way around a defender and tucked a backhand shot past Holtby for a shorthanded goal to make it 2-1 just 18 seconds into the second period.
Trading goals, the Stars then got the game tied again when Denis Gurianov scored on the power play to make it 2-2 at 1:46. Burning out the bulbs in the red lights, Patric Hornqvist then put the Panthers back on top when he set up shop in the slot and tipped in a shot from Gustav Forsling to make it 3-2 at 4:07.
Swinging momentum back in favor of the Stars in the span of just 28 seconds, Jason Robertson and Tyler Seguin then scored at 13:10 and 13:38, respectively, to make it 4-3. But with just 2:43 left in the period, MacKenzie Weegar finished off some great work from the fourth line with a goal to make it a 4-4 game.
"We don't want to trade chances," Barkov said of the action. "We want to control the game and play with the puck. Without the puck, we want to control the game. We're learning and we'll be better."
After Jamie Benn scored a go-ahead goal to put the Stars up 5-4 at 6:26 of the third period, the Panthers kept on pushing until, with Bobrovsky pulled for a 6-on-5 advantage, Jonathan Huberdeau threaded a long shot through traffic with roughly 29 seconds left on the clock to make it 5-5 and force overtime.
While both teams had some good looks during a very fast and furious extra frame of action, the game eventually to the shootout where Joe Pavelski and Robertson scored to secure the 6-5 win for Dallas.
"I thought we played a 50/50 hockey game on the road," Panthers interim head coach Andrew Brunette said. "I thought there were stretches where we played well and stretches where we didn't. It wasn't our A-game, but we found a way [to get a point]."
Sitting at 22-7-5, the Cats will wrap up their two-game road trip at Carolina on Saturday.
"Obviously we've been really good at home," said Barkov, citing Florida's stellar 18-3-0 mark in Sunrise. "We established that identity at home, but now we've got to figure out how to do it on the road now."
Here are five takeaways from Thursday's shootout loss in Dallas…