Berglund, who is 2 for 3 in his career on regulation penalty shots, also converted on Jan. 24 last season in a 3-2 loss to Pittsburgh.
"Maybe that's the only day I can score," he joked. "Hopefully, it comes up more often."
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.
Berglund was hauled down by Mike Fisher midway through the second period. Berglund faked a backhand, switched to his forehand and wristed a shot past goalie Pekka Rinne.
The goal, Berglund's second of the season, gave the Blues a 2-0 lead.
Berglund went into the breakaway without a true game plan, which he said contributed to his success.
"I had been thinking a whole lot about what I was going to do and I never scored on them," he said. "I just went in there, faked once and shot on the forehand."
Fisher, who was in the penalty box when the Blues scored their first goal, did not think his actions warranted a penalty shot.
"I got a piece of the puck. I don't think I got enough of him," Fisher said. "That's a tough call for the ref to make. That was a big goal for sure."
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. He made 14 saves in a 6-0 win over Detroit last Saturday.
Halak was not available for comment after the game, but his teammates were more than happy to sing his praises.
"Great bounce-back by him," Oshie said. "It's got to be tough (being pulled). It's got to wear on you a bit. You need a short memory."
Tarasenko, who made it 3-0 in the third period, has four goals and two assists in four games.
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.
After Berglund made it 2-0 in the second, Tarasenko stretched the lead with 10:56 left.
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. The Blues dominated play most of the night.
"Our players are starting to believe in the work part of the game," coach Ken Hitchcock said. "This was our best workmanlike effort and that's a good sign."
Nashville coach Barry Trotz acknowledged that his club was outhustled at times.
"You come into St. Louis, this is a bees' nest," Trotz said. "They get on you, they work as a group. We were not willing to play the type of game that you need to play to be competitive at this level."
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.
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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ST. LOUIS, MO - JANUARY 24: St. Louis Blues fans watch their team warm up before an NHL game between the St. Louis...