The Blues have won three of four this season, including a 4-3 shootout win in Nashville on Monday.
Vladimir Tarasenko and T.J. Oshie also scored for St. Louis, which has at least one point in 11 of its last 13 meetings with Central Division rival Nashville.
The Predators lost for the first time in regulation this season. They began the campaign with shootout losses to Columbus and St. Louis.
Halak, who made 13 saves, was pulled three days earlier after allowing three goals on 11 shots in Nashville. He rebounded to record his second shutout of the season and the 24th of his career. Halak made 14 saves in a 6-0 win over Detroit on Jan. 19.
Tarasenko, who made it 3-0 in the third period, has four goals and two assists in four games.
Berglund was hauled down from behind by Mike Fisher midway through the second period.
Berglund also scored on a penalty shot Jan. 24, 2012, in a 3-2 loss to Pittsburgh.
Oshie poked in a rebound of a drive by David Perron to give St. Louis a 1-0 lead midway through the first period. The power-play goal was the Blues' seventh of the season in their first 11 chances. Oshie has three goals in four games.
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St. Louis had 18 of the game's first 22 shots on goal and held Nashville without a shot for a stretch of 16:10 in the opening period.
Nashville goalie Pekka Rinne had lost only once in regulation in his previous seven games against St. Louis.
The Blues improved to 4-1-1 in their last six games at home against Nashville. The Predators have not scored in the last 182 minutes, 44 seconds of regulation play in St. Louis.
NOTES: Nashville is on a seven-game road trip, tying a franchise record, that ends Feb. 5 in St. Louis. The Predators also played seven successive road games from Oct. 30 to Nov. 12, 2002. ... St. Louis D Wade Redden played his first NHL game since April 11, 2010. He was signed by the Blues on Jan. 18. ... Predators RW Patric Hornqvist has five goals and eight assists in 19 games against the Blues. ... St. Louis is a league-best 32-6-5 at home since the beginning of last season.
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