Smith stopped 22 shots in his NHL debut, leading the Stars to a 4-0 victory over the Phoenix Coyotes on Saturday night.
"It brought back some memories," said Smith, who also had a shutout in his AHL debut last November. "I didn't feel as bad as I thought I would."
Mike Ribiero, Mike Modano, Phillipe Boucher and Darryl Sydor each scored for the Stars, who won for the seventh time on eight games to match the best start in franchise history.
"Everybody's contributing," Dallas coach Dave Tippett said. "We're playing pretty solid, playing percentage hockey, and getting the goals when we need them."
Smith struggled with what Tippett called "happy feet," misplaying the puck twice behind the net in the opening six minutes. The first time he was bumped off the puck against the boards, and the second time he tripped while trying to circle behind the net and had to lunge to clear the puck away from a Phoenix player.
Smith had a third close call when he stopped the puck on the goal line after Sydor tried to tip a short rebound into his goalie pads.
The 24-year-old otherwise benefited from a solid defensive effort that included a dozen blocked shots.
"I told our guys that they blocked more shots than me," Smith said. "When that happens you're going to win a lot of games."
Curtis Joseph made 28 saves for the Coyotes, who were shut out in consecutive games for the first time since March 24-26, 2004.
"It's not going to be handed to them," Phoenix coach Wayne Gretzky said. "They've got to fix it themselves. They've got to battle through it and got to figure out a way to get out of this. It's just not fun. The reality is, if you think we're better than our record indicates you better show it."
Phoenix, blanked 4-0 by Los Angeles on Thursday night, is off to its worst eight-game start (2-6) since opening the 1994-95 season 1-5-2 while in Winnipeg.
"We had a goalie there playing his first game and we let him see everything," Coyotes defenceman Ed Jovanovski said. "You could see the kid out there had some jitters. We have to get pucks to him and get people to the areas where it's tough to play and we're not doing that."
While Phoenix failed to capitalize on Smith's miscues, the Stars had little trouble when Joseph mishandled the puck midway through the second period. Joseph skated behind the net to slow a pass around the boards, only to watch the puck deflect off his stick to the front of the net.
Joseph dived to make a stick save on Jere Lehtinen's short attempt, but couldn't stop Modano's shot into the open right side of the net that gave Dallas a 2-0 lead at 11:58.
Boucher extended Dallas' lead to 3-0 at 3:52 of the third, one-timing a blast from the point under Joseph's glove for a power-play goal. Sydor made it 4-0 with 13:16 remaining on a rebound off a shot by Steve Ott.
Ribiero gave Dallas a 1-0 lead at 9:18 of the second period, beating Joseph off a long rebound from just below the right faceoff circle.
"We need our guys to be hungry around the net like that," Tippett said. "If the pucks are available, you've got to go get them."
Notes: Dallas also started the 1996-97 season 7-1-0. ... Modano has 83 career points against the Phoenix-Winnipeg franchise, his best total against any club. Modano has 32 goals and 51 assists in 76 career games against the franchise. ... The Coyotes were outshot for the first time in four games, 32-22. ... Phoenix is tied with Philadelphia for the most goals allowed with 33.