The Phoenix goalie had a career-best 44 saves, then denied the last four of five shootout attempts, and the Coyotes escaped with a 2-1 victory that solidified their shot for a second successive playoff appearance and perhaps home-ice advantage in the first round.
The Stars outshot Phoenix 45-27.
"We deserved to win tonight and we didn't get it," Dallas coach Marc Crawford said. "I told the guys after the game, 'You have efforts like that, you're going to win probably 98 percent of the games.' Their goalie was terrific tonight. He was the difference for them, and they needed every one of the saves that he got."
Bryzgalov, who had a shutout two games earlier but struggled through a 4-1 loss to San Jose on Saturday night, was asked how it felt to be facing such a barrage of shots on Tuesday. He pulled up his jersey to reveal a bare belly, then looked down and said, "I lose a few pounds."
Bryzgalov tied Bob Essensa's franchise record for most victories by a goalie at 129.
"It doesn't mean anything to me," he said. "I'm glad we got two points. It's more important for the team. I'm not chasing any records. It's not important."
Phoenix captain Shane Doan said Bryzgalov was "phenomenal" even as his team remains far from its best.
"But we can't rely on Bryzzy every night like that," Doan said, "even though he's been that good."
The victory kept Phoenix one point ahead of Los Angeles for fourth in the Western Conference, although the Kings have six games to go, to the Coyotes' four.
The Stars got one point to move into a tie with Calgary for ninth in the West, three points behind eighth-place Chicago.
Phoenix coach Dave Tippett said he could tell Bryzgalov was not about to have two bad games in a row. "He was a focused guy all day long, so you knew he was going to have a bounce-back game," Tippett said. "It's interesting. He's just got a focus on him. You can watch him in the morning skate. He was really dialed in."
Tippett noted most of the shots weren't close-range.
"He had lots of activity coming at him. I think he likes that sometimes," Tippett said. "If the shots are coming from outside and long-distance, he doesn't mind that."
Both teams scored in the second period.
David Schlemko's one-timer just after a power play put Phoenix up 1-0 with 7:51 left. Jamie Benn's 22nd goal of the season, on a power play, tied it with 2:26 remaining.
"Almost 50 shots," Lehtonen said. "I think we were the better team out there, which is a great thing. But we just weren't able to get many pucks past Bryzgalov."
The Coyotes, ending their second successive season under the NHL's ownership and with their future in Arizona uncertain, have won eight of 10. The hard-luck Stars have lost six of seven, one in overtime and two in shootouts.
Bryzgalov, who had tied his career best with 43 saves in a game against Detroit last Oct. 28, had 42 in regulation on Tuesday. He denied four of five attempts in the shootout. Ray Whitney's shootout attempt trickled under the pads of Lehtonen, the Dallas goalie falling on his backside as the puck entered the net.
Phoenix clinched the victory when Bryzgalov blocked Loui Eriksson's shot.
There were only three penalties in the game, none after the second period.
Coyotes LW Lauri Korpikoski missed his second game with an upper-body injury. ... Dallas was on the second stop of a five-game road trip, the last four in the West. ... Fiddler was back after sitting out one game with an upper body injury. ... Phoenix has played 78 games, most in the NHL.