The Stars have gone 2-0-1 since a five-game slide, picking up victories over Edmonton and Los Angeles in the middle of a four-game homestand before suffering a 4-3 shootout loss to Toronto on Friday night.
Radek Dvorak scored a game-tying goal with 7:13 left in regulation, but the Maple Leafs' Joffrey Lupul tallied the only shootout goal. His goal came after Jamie Benn hit the post on Dallas' second chance and Mike Ribeiro then failed on his attempt.
"I think we worked hard. It's too bad we just came out with one point, but I think that is shows we can play all 60 minutes," said Dvorak. "
Dallas was without captain Brenden Morrow for a second game in a row because of a back ailment and he is expected to miss a few more games.
After losing four of six to the Coyotes a season ago, the Stars have captured both meetings so far this year. The two wins have come in a shootout, with Ribeiro netting the winner at home on Oct. 10 before Trevor Daley tallied in the eighth round in Phoenix on Oct. 25.
That win was just the Stars' third in their last nine trips to the desert.
The Coyotes will try to get their offense going tonight after getting shut out by the Canucks 5-0 on Friday. Mike Smith yielded all five goals on 37 shots faced as Phoenix failed to score for a third time this season.
"When you have a game like this you just have to put it behind you and prepare for the next one," said Smith. "We weren't anywhere near as good as them tonight and it showed. Time to get back to work tomorrow."
Phoenix had won four of six coming in and conclude a three-game homestand. The Coyotes are likely to have Daymond Langkow for the first time in nine games after he was granted a leave of absence due to a death in the family.