The Coyotes rallied from a 3-1 deficit after two periods to earn a point on third-period goals by Oliver Ekman-Larsson and Ray Whitney, then had several excellent chances in the overtime. But Kari Lehtonen stopped all five Phoenix shots in the extra period, sending the game to a shootout.
"We need to play a team game," Stars coach Glen Gulutzan said. "We need to play for each other in that room. That's what gave us success when we went on our little run, and that's what's going to give us success in the playoffs. If we deviate from that, we're going to be in trouble."
After Coyotes' goaltender Mike Smith and Lehtonen made saves in the first round, Ribeiro raced in and made a perfect fake to get around Smith's poke check and put a backhander into an open net. Lehtonen stopped Whitney and Shane Doan for the win.
Lehtonen finished with 27 saves; Smith stopped 30 shots.
Dallas (40-28-5), which snapped a two-game losing streak, has 85 points and remains in first place in the Pacific Division. Phoenix (36-26-12), which began the night in seventh place, picked up a point and now has 84.
"I thought our guys came out with a mindset that we're just going to go hard at them in the third and find something. If you look at the last part of the game and the overtime, it's a game we deserved to win," Coyotes coach Dave Tippett said.
The Stars grabbed the lead 2:12 into the game when Loui Eriksson beat Smith to the short side with a breakaway wrister. Michael Ryder fed Eriksson, who streaked up the right side before burying a shot from the right faceoff dot for his 26th of the season.
However, that lead didn't hold for long as the Coyotes tied it up at 5:14 when Lauri Korpikoski took Whitney's passout from the right corner and fired a slapper past Lehtonen for his 16th goal of the season.
The Stars went on the power play for the first time at 4:43 of the second period when the Coyotes' Martin Hanzal was whistled for holding. Dallas capitalized 21 seconds later when Ryder knocked in a 15-foot slapper from the left side of the net for his career-high 31st goal.
"I think it's a suspendable offense," Gulutzan said. "He targeted the head with his elbow. The League will look at it for sure and then they'll decide, but it's deliberate."
Ryder made it 3-1 at 14:42 when he beat Smith from almost the same spot where he scored his first of the night. Eriksson and Ribeiro again got the assists.
Phoenix's Andrew Vermette was guilty of tripping the Stars' Radek Dvorak at 7:33 of the third, but it was the Coyotes who got a boost when Ekman-Larsson scored a shorthanded goal at 8:51 to make it 3-2.
Dallas gift-wrapped another golden opportunity for the Coyotes with 5:30 left when they had too many men on the ice. Phoenix took advantage 28 seconds later when Whitney beat Lehtonen top-shelf with a wrister from the slot for the equalizer. Doan got the assist after stealing the puck from Stars defenseman Sheldon Souray in the middle of the ice.
"I think we did some good things, but we got to find ways to keep that two-goal lead and not give those guys chances to get back in the game," Ryder said. "A couple of mistakes, a couple of turnovers and it ended up in our net, so we got to get a little better at that part."
The Coyotes had a chance to go ahead with 2:40 left in regulation, but Keith Yandle missed an open net. Dallas had a chance of their own at regaining the lead but Smith denied a wrister by Eriksson with 1:24 left to preserve the tie.
Midway through overtime, the Stars lost Benn after he was checked hard into the end boards by Vermette. Benn fell as he was making his way back to the bench before making his way down the tunnel to the locker room. He did return for the shootout.
Lehtonen came up big at 3:16 of overtime when he denied a shot by Ekman-Larsson with a diving pad save that sent the puck into the protective net behind the Stars' goal.
"Yeah, that's a really good save. I think I hit the pad there, so yeah, almost," Ekman-Larsson said.
The Stars lost defenseman Mark Fistric midway through the second period due to a lower-body injury and he did not return.
"(Fistric) has got a little bit of a pulled muscle, so we'll see how he responds tomorrow," Gulutzan said.
1 - 0 DAL
1 - 1 Tie
2 - 1 DAL
3 - 1 DAL