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.
Curtis Joseph made 28 saves for the Coyotes, who were shut out in consecutive games for the first time since March 24-26, 2004. 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.
Smith misplayed the puck twice behind the net in the opening six minutes, once when he was bumped off the puck against the boards and the second time when he tripped while trying to circle 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.
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.
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 club. ... 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.