Bozak took a cross-ice pass from Tarasenko in the third period and put the puck through the legs of Nashville goalie Juuse Saros. Tarasenko made the goal possible. He kept the puck inside the blue line to keep the play alive for St. Louis and then found a wide-open Bozak.
''It was kind of an accident. There's a bit of luck that's needed in these games and there was a kind of luck to that play,'' Tarasenko said. ''It was a big goal for us.''
Alex Pietrangelo added an empty-netter on the power play with four seconds remaining.
Binnington, a 25-year-old rookie, stopped 19 shots. All his shutouts have come since Jan. 7, when he made his first NHL start. He is 14-2-1 in that span.
''We were good tonight right off the bat, hot start,'' Binnington said. ''A couple chances didn't go our way, we didn't get it home, but we stayed with it the whole game and finally in the end there Bozie put one home. We're playing hard for each other and we're enjoying it. It's a special group in here and hopefully we can make the most of it.''
Bozak's big goal came a few seconds after a power play ended.
''We worked pucks hard that whole power play and obviously Vladdy made a great pass to me through the seam and I tried to shoot it quick,'' Bozak said. ''I knew there was a chance I could score and luckily it found a hole.''
Saros said he was paying attention to Tarasenko on the play.
''They moved the puck well and they had a one-seam pass and I was maybe over-anticipating one more pass in the middle,'' Saros said. ''I should have focused more on the shooter there.''
Nashville coach Peter Laviolette did not fault Saros, who finished with 42 saves.
''He played a great game. He did his job,'' Laviolette said. ''It just wasn't enough. We didn't have enough going the other way.''
St. Louis won the season series 4-1-0, taking the final four matchups from its Central Division rival. The Blues are 11-4-0 in their last 15 games against the Predators, who have a one-point lead in the division over Winnipeg.
The third-place Blues have three games in hand on Nashville.
''This is a team that we're behind,'' Bozak said. ''It's a team that we want to catch and possibly get ahead. Our goal is to keep moving up in the standings and keep getting better.''
St. Louis has won its past seven home games, the longest active streak in the league. The Blues also set a franchise record with 12 wins in February and matched their mark for any month (April 2013).
''We were in last place when January started,'' Tarasenko said. ''I don't know the stats. There's so many games. You move from one game to another. There's no thinking about how many you've won at home or on the road. We just try to win every game. We try to keep it rolling.''
Nashville got on the power play in the third when Colton Parayko was called for high-sticking at 8:08, but the Predators didn't get a shot during the two minutes. Right after the penalty, Parayko had a breakaway but Saros blocked the shot.
Binnington thwarted Filip Forsberg at 2:20 of the final period. Forsberg was all alone in front but couldn't score.
The Blues came right back with a big chance when Ryan O'Reilly hit the crossbar. However, the puck bounced straight down in the crease and out.
The teams battled through two scoreless periods. St. Louis controlled the action for the most part, outshooting the Predators 24-14. The Blues had one power play in the first period but Nashville killed it. The Predators were unable to score when they were on the power play in the second.
''Goalies are good and they're going to make saves,'' Blues coach Craig Berube said. ''That's part of the game. You have to stay with it and we did.''
NOTES: Blues LW Alexander Steen was scratched with the flu. St. Louis recalled Sammy Blais on emergency conditions from San Antonio. ... New defenseman Michael Del Zotto was a healthy scratch for the Blues. He was in Vancouver on Monday with Anaheim when the trade was completed and arrived in St. Louis late Tuesday morning. He has split this season between the Canucks and Ducks, scoring one goal and adding six assists in 35 games. ... The Predators made two moves Monday just before the trade deadline, acquiring Mikael Granlund from Minnesota and Wayne Simmonds from Philadelphia. Simmonds was in the lineup Tuesday but Granlund was not.
Predators: Play at Winnipeg on Friday.
Blues: Play at Carolina on Friday.
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