Lehtonen was outstanding, making 41 saves through overtime and stopping one of two shooters in the shootout. Only Brad Boyes scored against him in the tiebreaker.
"Sometimes it's this way," Lehtonen said. "In the first game of the year, I wasn't sharp. When one part is not doing well, another part helps out. I was able to make good saves, but the next night it might be another way."
Dallas (4-0), which overcame an early 2-0 deficit and was outshot 43-25, joined Toronto as the NHL's only undefeated teams. It was the Stars' second shootout victory this season.
James Neal and Eriksson scored in regulation to rally the Stars after Patrik Berglund and Andy McDonald staked St. Louis to its first-period lead.
"He was terrific, he gave us an opportunity to win," Dallas coach Marc Crawford said of Lehtonen. "He was super all night. He made it look easy because he moved so well. He was making believers of the guys in front of him. They started to dig in a bit more."
Eriksson's shootout goal was initially waved off, but a video review showed that the puck slid into the net under goalie Ty Conklin.
"I didn't think it was in initially," Crawford said. "On the replay it was evident that the goalie had just misplayed it. It's great that they have video review and ended up getting that right."
The Blues, who opened the season with two straight home wins, have lost two consecutive road games.
Eriksson had scored the tying goal with 5:17 left in the second period, when he took a backhanded pass from behind the net from Richards and roofed a point-blank wrist shot over Conklin's shoulder.
Neal had a goal and an assist for Dallas, and Richards chipped in with two assists to complete a big night for the club's top forward line.
"We're finding each other right now, we create a lot of chances out there," said Eriksson, who has four goals in four games. "We get two goals again and we've been playing really well lately, so I hope it's going to continue. I think everyone is really excited to get off to a good start here."
St. Louis outshot Dallas 14-5 in the third period and had a great chance to regain the lead early in the frame when Nicklas Grossman's delay-of-game penalty gave the Blues a 5-on-3 power play for 1:07. But St. Louis was unable to solve Lehtonen again.
Just seconds after coming out of the penalty box, Grossman was given four penalty minutes for high-sticking, but again the Blues failed to capitalize.
"We're not satisfied," Blues coach Davis Payne said. "I feel that type of performance is worthy of two points. In the third period on the five-on-three, we didn't get clean looks. We would have liked to score then."
St. Louis needed only 3:48 of the first period to take a 2-0 lead. Berglund connected 1:11 in, getting a stick on Boyes' wrist shot and deflecting it past Lehtonen. McDonald then scored on a power play, converting a cross-ice pass from David Backes for an easy tap-in at the left post.
"We started out well, I thought we really got the jump," Payne said. "We executed well even through the second period. We turned some pucks over and created turnovers."
The Stars made it 2-1 with two minutes left in the first on Neal's second goal of the season. Neal scored with a one-timer from the high slot off a pass from Eriksson that squeezed through Conklin, who was making his first start of the season.
NOTES: With Game 2 of baseball's AL championship series being played in nearby Arlington, the announced crowd was 11,750. That is believed to be the lowest crowd for a Stars' regular-season home game. The actual attendance was only about 7,000. ... Dallas winger Fabian Brunnstrom, who has been a healthy scratch for each Stars game this season, cleared waivers and was expected to be assigned to AHL Texas on Sunday. ... Dallas second-year forward Jamie Benn sat out his second straight game because of concussion-like symptoms.