Dallas had the edge in the first two games, beating Phoenix 4-3 in the season opener behind Jaromir Jagr's two goals and two assists, then in a shootout by the same score Friday night.
The Pacific Division rivals traded a few good scoring chances in a scoreless first period after the short turnaround and a couple more in the second before Phoenix broke through on a play set up by Smith.
Seeing the Stars building a big rush, the Coyotes goalie raced out of his crease to clear a puck along the boards. As he skated backward toward his crease, the Coyotes built a rush of their own, with Lauri Korpikoski finding Johnson along the left wing for a wrister that clanged in off the post.
Defensively, Phoenix barely gave the Stars room to move, much less get off shots.
With the Coyotes clogging lanes and diving in front of pucks, Dallas had six shots in the first period and one in the second before getting off two in the final minute.
That made it a little tough on Smith to keep his concentration, but he didn't mind.
"Obviously, it's nice to not have much action, but mentality it was definitely a test," Smith said. "It was nice to get through it."
The Stars created problems for themselves with penalties, giving Phoenix multiple chances with an extra man.
Dallas managed to kill six penalties, but was worn down by the third period, when Boedker punched in a rebound after a shot from the point by Derek Morris bounced off Richard Bachman to the side of the crease.
The Coyotes spent over 11 minutes on the power play, the Stars only 41 seconds.
"We paid for it before and we paid it for now," Stars coach Glen Gulutzan said. "We've had internal discussions about too many penalties and we're going to pay for it tomorrow in practice."
Bachman finished with 32 saves.
Notes: Coyotes LW Raffi Torres had a solid game and played aggressively after returning from a 21-game suspension for a hit that knocked Chicago's Marian Hossa from last season's playoffs. ... Dallas LW Ray Whitney missed a chance to play against his former team because of a lower-body injury that sent him to the injured list. Dallas recalled rookie RW Reilly Smith to fill his roster spot.