Dallas took a 1-0 lead at 13:55 of the first period when Robertson scored on the rebound of his own shot from the top of the crease.
Seth Jones tied it 1-1 at 4:22 of the second period on a shot from the right face-off circle. It was his first game since sustaining a broken thumb in Chicago's 4-3 overtime loss to the Buffalo Sabres on Oct. 29.
Andreas Athanasiou gave the Blackhawks a 2-1 lead at 13:53 after he beat Stars defenseman Miro Heiskanen to the net.
Connor Murphy made it 3-1 at 16:53 after the puck came loose in a net-front scramble, and Domi extended the lead to 4-1 at 9:37 of the third period on a diving effort.
"We've just got to learn how to play with the lead," Jones said. "We've got to defend hard and make the little plays that win you hockey games, getting pucks in, getting pucks out of our zone. They obviously turned up the pressure and we couldn't handle it."
Jamie Benn, who had a goal and an assist, cut it to 4-2 on the power play at 10:15 with a wrist shot that beat Mrazek blocker side. Mason Marchment then scored to make it 4-3 at 13:58 on a one-timer from the left circle.
"It was a good team effort to come back," Marchment said. "We were winning battles in the third there, and it was making it easier for us to transition and turn to offense there."
Ty Dellandrea tied it 4-4 at 14:12 when he redirected a point shot from Jani Hakanpää.
"We didn't have the same work ethic [in the third period] and sat back a little bit," Chicago coach Luke Richardson said. "Not trying to preserve [the lead] but they were coming hard, and we just didn't handle it well. They got some momentum and they started coming, and they're a very good offensive team.
"We just didn't handle it well. Unfortunately, I thought the guys worked really hard for 40, 50 minutes, but the game's 60 minutes. That's just a tough lesson to learn that we can't sit back."
Faksa's goal at 18:27 gave the Stars a 5-4 lead, scoring from a sharp angle on the goal line.
"I wasn't sure because I kind of was behind the goal line," Faksa said. "I knew at least half the puck was in, but couldn't tell if it was all the way. Right away when I [got to] the bench, they told me it was in. It was a big relief and a big turnaround.
"It's even [better] when you're at home. You can feel the fans and they're just pushing you. Every goal it was [getting] louder and louder, and we were just going to win for them."
Robertson scored into the empty net with nine seconds left for the 6-4 final.
NOTES: Stars defenseman Ryan Suter played his 1,300th career NHL game. ... Blackhawks forward Jonathan Toews got his 500th NHL assist on Murphy's goal. ... Chicago forward Sam Lafferty did not play in the third period due to soreness. Richardson said he will be reevaluated Thursday.
