St. Louis earned its first regulation win in four tries against the Wild and improved to 8-3-1 in its last 12 at home.
"He's been the best player for our team for a long time and he played a good game today as well," Lehtera said of Elliott. "That's nothing special anymore."
Mathew Dumba scored late in the second for the Wild, who lost their 10th game in their last 11.
Elliott improved to 7-3-2 since taking over for the injured Jake Allen (lower body), including making 23 saves in the second period. The Blues had averaged just 1.99 goals a game for Elliott in the previous 11 games.
"It's awesome when the guys are putting it in," Elliott said. "You just kind of get uplifted. I think the whole bench feels it and you just kind of keep going and get on that good feeling train."
Minnesota's 24 shots in the second period set a franchise road record for any period, and was St. Louis' season high for shots given up in a period.
"When you put the right effort and you put the right attitude into the game, then you bring something that you can take some pride out of," Wild coach Mike Yeo said. "That's something that you can build off of and that's what we need to do right now."
Tarasenko's power-play goal at 2:47 of the second gave the Blues a 1-0 lead and broke an 0-for-24 slump for St. Louis on the man advantage. It was also Tarasenko's fifth goal in his last six games against the Wild.
"You could almost hear the collective sigh on the bench (after Tarasenko's goal)," said assistant coach Brad Shaw, who spoke to the media instead of coach Ken Hitchcock after the game.
It took the Blues just 8 seconds into their next power play to convert when the puck went off Lehtera's leg to make it 2-0 at 9:19 of the second.
Stastny scored his 12th goal and recorded his 34th career point in 53 games against the Wild at 16:51 of the second.
The three-goal second period by the Blues equaled the team's total offensive output for the previous four games.
Brouwer's goal early in the third period was the Blues' third power-play goal of the game. It's the first time since Jan. 6, 2015, that the Blues scored three power play goals in a game.
"The execution was a lot sharper," Shaw said. "I thought we were a lot more direct in our game. We were way more decisive, way more in sync."
Dumba's power-play goal late in the second gave him two goals and two assists in three games since the All-Star break.
Wild goalie Devan Dubnyk entered with a 2-0-1 record against the Blues this season with a .935 save percentage, but stopped just five of eight shots in the second period as the Blues broke it open.
"It's tough to sleep at night, it's hard to let it go on days off, but this is the situation," Dubnyk said. "It happens sometimes during years and you've just got to stay working and find a way out of it."
The Wild recalled F Tyler Graovac from the Iowa Wild of the American Hockey League and placed D Jonas Brodin on injured reserve. Brodin is expected to miss 3-to-6 weeks with a broken foot suffered on Feb. 4. ... Blues D Alex Pietrangelo notched his 20th assist of the season Thursday. Pietrangelo has at least 20 assists in each of his first five full NHL seasons. ... Wild F Jason Zucker and F Thomas Vanek were healthy scratches. Vanek (14 goals) and Zucker (11 goals) are two of the team's top four goal-scorers this season. ... Blues F Scottie Upshall picked up his 500th career penalty minute with a high-sticking minor late in the first period.