Eriksson's first career hat trick gave him five goals in two games, helping the Stars to a 6-5 victory over the Columbus Blue Jackets on Thursday night.
Eriksson's breakout season has been one of the few positives for the injury-riddled Stars. Eriksson has already established a career high with 17 goals.
"He's one of those guys who you look to do the job, and he comes through no matter what," Stars coach Dave Tippett said. "We had him penciled in for 20-plus (goals). We knew he had the potential and he's doing a heck of a job. He's had timely goals that have given us life."
All three of Eriksson's goals came from close range. He's one of the few Stars with the ability to get to the net and finish plays.
"I'm trying to be more (in front of the net) and the puck is going in right now," Eriksson said.
In the shootout, Richards and Ribeiro beat goalie Pascal Leclaire in the first and third rounds to lift the Stars to their sixth win in nine games. Columbus' Kristian Huselius hit the right post in the first round, and Marty Turco stopped Rick Nash in the second.
Richards added a goal and three assists, and James Neal had a power-play tally for the Stars.
It could have been a bit of a letdown for Columbus, coming back 24 hours later to face the team with the second fewest points in the Western Conference.
"We played the best team in the league and came back and won in overtime and almost came back and did the same thing tonight," Huselius said. "It was a weird game."
The Blue Jackets thought they netted the winning goal 13 seconds into overtime on Manny Malhotra's apparent goal, but after a video review, officials ruled the puck was kicked into the net.
Columbus coach Ken Hitchcock was seething after the game, contending the officials blew the call on Malhotra's no-goal.
"We won the hockey game," Hitchcock said. "It was a good goal. They can put up whatever score they want. That player did not try to kick it in. It was a great victory."
Hitchcock took one more question from reporters, then left, saying, "You're not listening to what I'm saying, we won the hockey game."
Malhotra agreed with his coach.
"It's a frustrating way to lose a point," Malhotra said. "I'm a half-decent soccer player and I couldn't have tried to kick that in."
Dallas held a 5-4 lead with less than three minutes remaining in regulation, but Nash tied it with 2:46 left when he scored from close range off a pass from Fedor Tyutin.
Nash scored 1:34 after the opening faceoff, firing the rebound of Umberger's shot past Turco while Columbus had an extra attacker due to a delayed Dallas penalty.
Dallas drew even at 1 at 3:57 of the first period, while the teams skated 4-on-4, when Eriksson knocked Richards' centering pass past Leclaire.
Brassard put the Blue Jackets in front 2-1 on the power play, skating around the Dallas defense and beating Turco from in front at 10:02.
Eriksson tied it at 2 with two seconds left in the first, scoring from in front off Joel Lundqvist's setup.
Eriksson completed his hat trick on a rebound 1:20 into the second while the Stars had a 5-on-3 power play.
Neal gave Dallas a 4-2 edge on a power-play deflection 1:19 later.
Columbus pulled within 4-3 at 2:39 of the second period when Umberger scored off Nash's goal-mouth pass.
Richards backhanded a loose puck past Leclaire at 8:57 of the second period to restore Dallas' two-goal advantage, but Huselius' goal at 14:38 of the second made it 5-4.
"It was a tough game emotionally last night and we came here and stole a point," Nash said. "They were a desperate hockey team and so are we."
Notes: Eriksson scored five straight Stars goals over the two-game span to match the franchise record set in 1973 by Dan Grant when the team played in Minnesota. ... Columbus lost its first 10 games in Dallas after joining the NHL, but the Blue Jackets have won four of the last six. ... Leclaire assisted on Brassard's goal, the first point by a Columbus goalie this season.