Curtis Joseph made 34 saves for Phoenix to hold up his end of the goalie showdown, but Morrow's second-period goal was the difference. The Stars captain took a pass from Sergei Zubov just to the right of the crease and flipped the puck over Joseph's glove and into the top corner of the net 2:09 into the period. The goal came just 18 seconds after Jeremy Roenick was sent off for stick holding.
Turco did the rest in posting his 25th career shutout and first in 19 career games against the Coyotes.
Phoenix has been shut out three times this season, twice at home by the Stars.
Turco was rarely tested over the first two periods, facing only seven shots including just two in the first frame. His best save came early when he dived to the ice to poke check the puck away from Enver Lisin before the rookie could take a shot on a breakaway.
He also got some help from the post as Ed Jovanovski blasted a shot off the crossbar with 14:58 remaining.
Joseph kept the Coyotes in the game, especially in the first 40 minutes when he made 28 saves. He had been pulled from his previous two starts after allowing seven goals on 24 shots.
Notes: The Coyotes' 13 shots were a season-low and only two above their fewest in franchise history. Phoenix had a season-worst two in the first period. ... Turco hadn't had a shutout since Dec. 29, 2005, against St. Louis. ... Dallas G Mike Smith shut out the Coyotes 4-0 on Oct. 21 in his first career start. ... Phoenix has allowed 25 power-play goals in its last 16 games. ... Phoenix was 0-for-5 on the power play. The Stars have allowed only one man-advantage goal in 25 opportunities over five games. ... Coyotes RW Mike Ricci skated during practice Thursday for the first time since injuring his neck in the pre-season. If there are no setbacks, Ricci could return to the lineup in three weeks.