Nashville (42-26-5) has moved into commanding position for a playoff spot behind Rinne, who has posted a 1.15 goals-against average and a .959 save percentage in winning the Predators' last six games. He has doubled his shutout total this season to six -- fifth-most in the NHL.
Rinne's strong weekend helped put the Predators within a victory of their season-best seven-game winning streak from Nov. 12-25. He made 33 saves in a 1-0 overtime win over visiting Columbus on Saturday before a 23-save effort in Sunday's 3-2 victory at St. Louis.
He's gone 131 minutes, 36 seconds since last allowing a goal at home.
Rinne has given up four even-strength goals in the last six games, with five victories coming by one goal. One of them came Sunday when the Predators rallied from a 2-1 deficit with under 4 minutes left.
"We showed a lot of character, we showed a lot of poise at the end," Rinne said. "We didn't panic."
Dustin Boyd and Patric Hornqvist scored 48 seconds apart Sunday, with Boyd's second goal of the contest the game-winner with 2:46 remaining. The Predators outshot the Blues 16-7 in the final period.
Hornqvist, who has three goals and two assists in five games, was encouraged with Nashville's strong play in the third.
"I think that was the best period for a long, long time," Hornqvist said. "If we keep working like that, we're going to get lots of points down the stretch."
Rinne has started against Dallas (31-27-14) once, making 27 saves in a 4-2 victory Oct. 31. The Predators have won two of three against the Stars this season, with all the meetings in the season's first month.
Dallas completed a 2-2-2 homestand with a 3-2 overtime loss to surging Phoenix on Sunday. Jamie Benn and Loui Eriksson scored to rally the Stars from a 2-0 deficit.
"Give our guys lots of credit," coach Marc Crawford said. "No quit in them. They kept fighting. They battled hard. We got a point out of it, but at the same time, those things just crush you."
Dallas unsurprisingly had trouble with its penalty kill on the homestand, allowing eight goals in 24 chances. The Stars have one of the worst units in the league at 76.0 percent and gave up two power-play goals Sunday.
"We didn't do a good enough job killing penalties, although we did get a couple of big kills late in the game," Crawford said.
The Predators, though, have one power-play goal in their last 10 opportunities.
Nashville is 10-4 with one tie in its last 15 home games against Dallas, with three straight wins.