Pekka Rinne and the rest of the Predators' defense made sure Nashville needed only a bit of scoring to win.
Despite leading scorer Colin Wilson and top-six forward Patric Hornqvist being out because of upper body injuries, the Predators snapped a six-game, road-losing streak (0-5-1) on the first stop of a five-game trip.
"It's a huge trip for us. It's obviously nice to get that first game right away, get a big win. This is what we needed," said Rinne, who has allowed one goal over his last three outings. "We scored timely goals, and our penalty kill tonight was really good. I think it was a strong game defensively."
Kari Lehtonen made 17 saves for the Stars, who had scored at least three goals in 13 of 15 games. Dallas, which was shut out for the third time this season, has one goal in its last two games after totaling 19 in the previous five.
"Certainly, we needed to be a little bit better in a bunch of areas," Stars coach Glen Gulutzan said. "We played soft, we didn't go to the hard areas to score, we didn't force it down their throat. We just thought, `Maybe we'll get some fluff or get a bounce, maybe one will come to me at the back door, whatever.'
"You've got to jam it down their throat, come after them."
Nashville scored on two of four power plays and turned aside Dallas' four advantages. The Predators are 5-for-10 on the power play in their last three games after a 1-for-14 slump in the previous six.
"We need our special teams to be good, and they ended up being pretty good on both ends," Nashville coach Barry Trotz said. "The best penalty killer was obviously our goaltender, who was outstanding. But a lot of guys contributed. You just had a lot of people step up, a lot of the younger guys are stepping up."
Although veteran forward Ray Whitney returned after missing 16 games because of a broken foot, the Stars were without top-line center Jamie Benn (wrist) and captain Brenden Morrow, who sat out a second game (groin).
The Stars began a season-high, four-game homestand as part of a stretch in which they will play nine of 11 in Dallas. They fell to 5-5-1 there.
"Every game is important now, especially the home games," Stars winger Loui Eriksson said. "I thought we had some really good chances. I don't know, we just have to be better to score the goals there."
With the Predators leading 2-0 midway through the second period, Clune scored on a penalty shot at 9:09, firing a wrist shot through Lehtonen's pads. It was the first penalty shot for Clune, a former Stars draft pick who never played for them.
"I was kind of thinking shot the whole way," said Clune, who earned the penalty shot when he was hooked by Jordie Benn on a breakaway. "The ice is a little chippy here in Dallas, so I didn't want to deke and fumble on the puck. I was thinking either low blocker or five-hole, and he was pretty far back in his net."
Dallas' best scoring chance came with 3:17 left in the second, when Whitney set up Trevor Daley for a one-timer from the slot. Even though he had a half-empty net, Daley's shot hit teammate Erik Cole in the skate before Rinne dived across to knock away the rebound.
"It was just a scramble play, but sometimes you have to be lucky, too," Rinne said. "It was a wide open net, and he put it on the ice, and I was able to get it. I was a little bit lucky, too."
An outbreak of fights erupted with 5:35 remaining in the third period during a Nashville power play after Mike Fisher crashed into Lehtonen. Stephane Robidas challenged Fisher to a fight, and two more bouts broke out elsewhere.
Just 33 seconds later, Bourque scored his seventh goal.
Spaling got the all-important first goal with a shot that beat Lehtonen's glove at 12:16 of the first period. It was his fourth of the season.
Weber's fourth of the season appeared to glance off the stick of Jordie Benn in front and just inside the left post at 2:16 of the second.
"We made some young errors, had some turnovers, especially with our D," Gulutzan said. "We need our big guys to step up when those situations happen, to take control, and we didn't do it."
The Stars responded with considerable pressure, but Rinne made outstanding saves on Whitney's one-timer from the left circle at 3:15 and on Eriksson's one-timer from the right circle at 4:38.
Predators C Paul Gaustad left the game after the second period with an upper body injury and didn't return. ... Wilson, who leads Nashville with seven goals and 19 points in 25 games, was injured Saturday against Minnesota. He is expected to be out at least through the weekend. ... The Stars honored former RW Bill Guerin, who spent three seasons with Dallas from 2002-06, by putting him on the club's all-time team. Guerin had 72 goals and 159 points in 216 games with them. ... The Predators are 10-0-5 this season when they score first. Dallas is 1-10-1 when its opponent strikes first.