"For whatever reason, you have success against them one year and we'll take the victories we've had against them this year," Kariya said.
Kariya scored his 28th goal and rookie Shea Weber got his first in the Predators' seventh victory over the Blues this season, a 3-0 win Thursday night.
The Predators are perfect against the Blues with one game remaining between the Central Division foes.
Nashville has lost six of its last eight games with the two wins coming against the Blues.
The Blues have lost a franchise-record 12 straight games, and were shutout for the fifth time this season. Earlier this season, the Blues lost 11 in a row from Oct. 20 to Nov. 12, a streak that started and ended with road losses to Nashville.
"It's frustrating but we've put ourselves in this mess," St. Louis forward Keith Tkachuk said. "We know the situation we're in. We're not going to lay over. We've got to keep going. We've got to find a way out of this hole."
Nashville goalie Chris Mason recorded his first shutout of the season and second of his career. Mason turned aside 18 shots.
All of Nashville's goals came on the power play.
"We got a real good work ethic going, established a good forecheck, played solid through the neutral zone and obviously special teams were really good for us on both ends," Nashville coach Barry Trotz said. "I just thought we managed the puck all night pretty well."
Nashville's Kimmo Timonen, who also had an assist, scored his 11th goal of the season at 8:10 of the first period. The Predators dominated action by outshooting the Blues 12-4 in the first period.
The Predators made it 2-0 in the second period when Weber scored at the 15:04 mark. Yanic Perreault, who had three assists, fed Weber, who blasted a slap shot from just inside the left circle. The goal came in Weber's 23rd game.
"It's huge. As a kid you always dream of getting a goal in the NHL," Weber said. "In the situation we're in right now, it was a pretty big one for us and hopefully we can keep on rolling heading into the playoffs."
Kariya scored at 5:36 of the third period, putting back his own rebound from the right of the goal after St. Louis goalie Reinhard Divis blocked his first attempt.
Nashville had seven power-play attempts.
"We gave them too many chances on the power play, that's for sure," Divis said. "That hurt us."
The Blues, who had four power-play opportunities, are 0-for-18 with the man advantage in their last three games.
"This wasn't one of our better efforts," St. Louis coach Mike Kitchen said. "We try to win every game and we'll keep trying."
Nashville goalie Tomas Vokoun (36-18-7) was scratched for the third game with a sore back. ... St. Louis assigned goaltender Chris Beckford-Tseu to its American Hockey League affiliate, the Peoria (Ill.) Rivermen and actived goalie Jason Bacashihua off the injured reserve list. ... The Blues are 0-30-5 when trailing after two periods while Nashville is 27-1-4 when leading after two periods. ... In addition to the 12- and 11-game losing streaks, this season the Blues also have had a nine-game losing streak.