Weber scored his second goal with a straightaway shot midway through the third period, answering the homestanding Hurricanes' final-period flurry and helping the Predators take a 5-2 win on Sunday.
Jason Arnott also scored two goals for the Predators, who scored the first four goals and never trailed in ending a two-game losing streak. Scott Nichol had the other goal for Nashville and Dan Ellis finished with 24 saves.
The only hiccup was allowing two goals by Carolina in the first 6 1/2 minutes of the third period that made the game closer than coach Barry Trotz would have liked.
"We were hoping to do a little better job than that," Trotz said. "I think (Ellis) played pretty good and we were hoping maybe we could secure maybe a shutout. We talked about keeping the opposition, especially on the road, to two goals and we'd have a chance to win. And we did that."
The Hurricanes had won three straight games coming in, but didn't mount much of a challenge early. The Hurricanes went 0-for-5 on the power play in the first period, including almost 2 minutes worth of 5-on-3 play. The Predators took advantage of their chances, using Arnott's goal on a 2-on-1 chance to take a 1-0 lead into the first intermission.
Then came three more scores, with Weber getting his first goal by burying a shot from the left side past Cam Ward midway through the second period. Arnott ended the spurt, scoring when his shot near the crease appeared to bounce off Carolina defenseman Joni Pitkanen's skate and past Ward for the 4-0 lead with just under six minutes left in the period.
Both teams figured that opening period ended up being the difference - Carolina for its missed chances, Nashville for its effective penalty kill.
"That really boosted up the momentum," Weber said. "The guys see the penalty killers doing a great job out there and really sacrificing their bodies. To come out of two 5-on-3s and not give up a goal is pretty rare, so we were fortunate."
Added Ellis, "I know I didn't have to make many saves."
The Hurricanes managed just 16 shots through the first two periods despite having seven power plays.
"It just kind of set the tone for the game," Hurricanes coach Peter Laviolette said. "It was a reflection of our game."
Matt Cullen had a goal and an assist for the Hurricanes, while Chad LaRose also had a goal that cut the deficit to 4-2 and got an otherwise frustrated home crowd back in the game. But just as the Hurricanes killed off a tripping penalty on Niclas Wallin, Weber fired the shot from near the blue line into the upper right corner of the net to push the margin to 5-2 with 7:18 left.
"You put yourselves in that hole, it's hard to overcome," Cullen said. "We gave ourselves a chance, but it was a little too late to come out as flat as we did."
Notes: Nashville is 7-2 when scoring first this season, while Carolina is 7-4-1 when its opponent scores first. ... The Predators will return home to face St. Louis before facing another Southeast Division team - Atlanta - on the road on Wednesday. ... RW Martin Erat had two assists for Nashville. ... Cullen's goal was his first since Oct. 28 at Montreal. ... Ryan Bayda's assist on Cullen's goal ended a five-game streak without a point. ... Carolina D Tim Gleason suffered a lower-body injury in the second period and didn't return for the final 20 minutes. ... Carolina RW Patrick Eaves also left with what appeared to be an upper-body injury.