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Jamie Benn tied it with his first career short-handed goal earlier in the third, and Benn's pass set up Ribeiro's winner.
With the game tied at 2, Brenden Morrow got possession on a forecheck and fed Benn, who flipped a pass across the goal-mouth to Ribeiro. Ribeiro skated in from the left side and fired high over goalie Jaroslav Halak.
"He was real good tonight," Dallas coach Marc Crawford said. "It was nice to see him get such a feed from a play that he's usually making to a teammate. It was nice to see that one going in."
Ribeiro, who opened the season with a 16-game drought, has three goals in his last five, including a pair of winners.
Ribeiro, tied for the team lead with 16 assists, knows he needs to pick up the goal-scoring as the center on the second line.
"The thing is to keep working and create chances," Ribeiro said. "If I can do that enough, the scoring will be up."
Richards scored his team-high 11th goal and Kari Lehtonen stopped 25 shots for Dallas, 4-1-1 in its last six.
Andy McDonald had a pair of goals, the first one short-handed, and Halak made 19 saves for the Blues, whose three-game winning streak ended.
The Blues capitalized on a penalty kill when McDonald knocked a rebound past Lehtonen at 5:07 of the first period. The Stars got stuck deep in the St. Louis zone, and McDonald cashed in on a 3-on-2 break with 48 seconds left on a Dallas power play.
Richards tied it with a wrist shot into the upper right corner of the net at 10:53 of the second period, capping about 45 seconds of Stars' possession in the Blues' zone.
McDonald struck on a seemingly innocent wrist shot from the left circle that dribbled through Lehtonen's pads with 4:20 left in the second period for a 2-1 lead.
Benn tied it at 2 at 7:53 of the third period on an outstanding individual play.
Benn stole the puck from Erik Johnson at the Dallas blue line, skated in alone and tapped a backhander past Halak with 6 seconds left on a St. Louis power play.
"I think [Johnson] was just trying to make too many moves," Benn said. "I poked it away and scored my goal."
The teams will complete a rare home-and-home, back-to-back set Saturday night in St. Louis, and McDonald said the Blues must do a better job of protecting leads than they did Friday night when Dallas rallied twice.
"We didn't have our best third period," McDonald said. "We didn't generate enough in the third. We were sitting back a little bit. We didn't respond."
Both teams stepped up the physical play late in the second period, and the Stars anticipate more of the same in St. Louis.
"There was a reason why at the end of the period they came after us. When you know you're going to play the same team the next day, they want to send a message," Stars defenseman Stephane Robidas said.
The Blues are without RW T.J. Oshie (ankle), LW David Perron (concussion) and D Roman Polak (wrist). ... Earlier in the day, Dallas placed D Mark Fistric on IR because of a groin injury, with Jeff Woywitka moving in as his replacement. Rookie D Severin Blinderbacher, called up from the AHL earlier in the week, was a healthy scratch and will have to wait to make his NHL debut. Fistric was hurt at a practice this week in Toronto. ... Richards scored his first career goal in 15 games against St. Louis. ... Dallas RW Loui Eriksson is tied for second on the team with nine goals, but hasn't found the net in his last nine games.
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DALLAS - NOVEMBER 26: Brad Richards #91 of the Dallas Stars heads to the ice for warm ups against the St. Louis...