These struggling Central Division rivals split those contests, and the Predators will look to get off to a better start Monday night against the visiting Stars.
Nashville (21-22-7) is allowing 0.94 goals per game in the first period, the third-worst mark in the NHL. It fell behind 3-0 after one and trailed by four in the third in a 5-4 home defeat to Colorado on Saturday.
"There's a lot of will on our team, there's a lot of fight," coach Barry Trotz said. "We've had a year in which we've had a lot of heartache. I think this is the sixth game we were down 3-0 in the first period, a lot of times it has nothing to do with the way we're playing."
The Predators were outshot 14-8 in the opening 20 minutes and will look to avoid giving up the first goal in their third 2013-14 meeting with the Stars. Nashville rallied for a 3-1 home victory over Dallas (21-19-8) on Dec. 12 before falling 4-1 on the road Dec. 27.
The Stars are enduring a miserable month in which they've gone 1-7-1 with the lone victory coming Tuesday over Edmonton, the worst team in the Western Conference. They are 0-3-1 in their last four on the road after a 3-2 overtime defeat to Minnesota on Saturday.
Alex Chiasson scored on the power play to tie the game in the third period, and Dallas finished with a 35-19 edge in shots.
''It's disappointing,'' Chiasson said. ''This was probably one of our best games defensively, as far as scoring chances given to the other team. It's just a little play there, and that's tough. We battled through and it would've been nice to get a win here.''
Top scorer Tyler Seguin has four points in a three-game run, but has been held without any against Nashville this season.
The loss dropped the Stars nine points behind the Wild, who are tied with Vancouver for the last two playoff spots in the West. Dallas coach Lindy Ruff is trying to stay positive ahead of this back-to-back set of games that includes Tuesday's home rematch with Minnesota.
"We still can gain some ground, a couple games here real quick," said Ruff said. "We can get it down to five (points) or six."
Trotz could give Devan Dubnyk his second start with the Predators. Dubnyk, acquired Wednesday from Edmonton, made 24 saves in his Nashville debut Saturday.
''He got nervous and was rusty," Trotz said. ''I know Dubnyk has been in the league a long time, and I've seen a lot better games from him. But it was his first game. We gave him very little support early, and it just looked like he was nervous after that.''
Dubnyk is 1-5-1 with a 3.15 goals-against average in seven starts against the Stars.