The Blues escaped Madison Square Garden with a 4-3 win Monday despite getting thoroughly outplayed by the New York Rangers in the first period and giving up back-to-back goals to Martin St. Louis in the third.
Tarasenko beat Rangers goalie Cam Talbot in the bottom half of third round of the shootout after Blues goalie Brian Elliott stopped Rick Nash with a pokecheck in the top half. Blues forward Alexander Steen and Rangers forward Lee Stempniak scored in the second round.
The Blues have won five in a row since a two-game losing streak. They play Tuesday at the New Jersey Devils. The Rangers have lost back-to-back shootouts and are 1-1-2 since a three-game winning streak. They play Wednesday at home against the Detroit Red Wings.
"He's as dynamic of a goal-scorer as anyone I've ever played with," Blues captain David Backes said of Tarasenko, who has scored six goals in the past four games. "His shot and his burst of speed and his ability to find the net obviously is out of this world."
Nash had multiple chances to end the game in overtime. His first came at 45 seconds, with the Rangers on a power play, but his shot from inside the left circle hit the right post, came out and was covered by Elliott. The play was reviewed to make sure the puck hit the post.
"I didn't think it went in at all, so I didn't even know why they were looking at it," Elliott said.
Nash's second chance came with 1:16 remaining in overtime, when he got the puck at the bottom of the right circle and tried to wrap it around Elliott's pokecheck while falling through the crease. The puck hit Elliott's right skate and went wide to the left of the net.
"We had some great chances in overtime. It would have been nice obviously to get one there on the power play," Rangers defenseman Marc Staal said. "Having the lead, giving that up, it's frustrating. We had the chance to win the game in regulation. We just didn't do it."
The game got to overtime after a seesaw third period in which each team scored twice, took the lead and gave it up.
St. Louis' first goal came at 6:28; it tied the game at 2-2. His second goal, at 13:17, gave New York a 3-2 lead. It lasted for 76 seconds.
Bouwmeester erased the deficit when he took a drop pass from center Jori Lehtera and roofed a shot from between the circles and above the hash marks over Talbot's blocker and into the top left corner of the net at 14:33 to tie the game at 3-3.
It was Bouwmeester's first goal of the season and first since Jan. 20.
"There was no one in front of me, so I looked up and that's where I shot it and I wanted to shoot it there," Bouwmeester said. "A lot of times my shots don't go where I want them to, but that was good."
Berglund gave the Blues a 2-1 lead at 3:50 of the third period with his first goal of the season. The puck went in off his left skate after Barret Jackman's one-timer from the right point initially hit off of Rangers center Chris Mueller's stick.
"That's a big lift, a big burden off his back," Blues coach Ken Hitchcock said of Berglund. "Hopefully he can get some positive energy and get playing at a high level again."
The Blues knew they were playing at a low level in the first period, when the Rangers dominated possession and got a power-play goal from Chris Kreider to take a 1-0 lead at 5:29. New York had a 15-4 edge in shots on goal and 27-13 advantage in total shot attempts.
Hitchcock called it the worst period the Blues have played this season, and said it was noted in the dressing room between periods.
"We said a few words, yeah," he said. "We had a fireside chat."
New York coach Alain Vigneault said the first period was one of the best the Rangers have played, particularly considering they were playing with their backup goalie in net and without four of their top-six defensemen and a top-six forward because of injuries and a suspension.
"I think we made the mistake of looking at who was out with the Rangers instead of who was in," Hitchcock said. "That's a huge mistake because their forward group is really dynamic, the fastest group of forwards that we've played all year."
The Blues got back to playing their grinding, possession style in the second, when they outshot the Rangers 17-8 and out-attempted them 25-14.
Tarasenko tied the game at 7:18 of the second period with a show-stopping, goal-of-the-year candidate with the Blues on the power play.
He picked up speed in the neutral zone, got the puck at the red line from defenseman Kevin Shattenkirk, and left all four Rangers penalty-killers in his wake before beating Talbot with a one-handed shot.
In fact, Tarasenko was surrounded by the four Rangers penalty-killers when he crossed the blue line, but he blew past a diving Michael Kostka, split through forwards Tanner Glass and Nash, and made a move that froze defenseman Dylan McIlrath. Once in behind the Rangers, Tarasenko deked to get Talbot moving toward the left post before reaching back with his right hand on his stick to knock the puck into the net, between Talbot's left skate and the right post.
"Yeah, it's not a bad play that he makes," Backes said, laughing. "I'm the stretch guy on that power play and I think I had the best seat in the house to watch it."
And what was Backes thinking when Tarasenko hopped over the boards with a chance to ice the game in the third round of the shootout?
"I haven't got his moves down quite like I do [T.J.] Oshie when he's going, but you know he's dynamic," Backes said. "He's either shooting it quick or he's got a couple of dirty moves that you never know when it's going to come out.
"Great win, found a way."
Follow Dan Rosen on Twitter at: @drosennhl