Minnesota had the upper hand on St. Louis for most of this series, controlling the play for periods at a time.

With goalie Jake Allen as their guide and coach Mike Yeo on their side, though, the Blues sure had the right formula for beating the Wild in the playoffs.

Magnus Paajarvi scored at the 9:42 mark in overtime, giving the Blues a 4-3 victory on Saturday in Game 5 of their playoff series to eliminate the Wild in the first round following the best season in franchise history.

“They know us. We know them,” said Allen, who stopped 174 of the 182 shots he faced. “They got the best of us two years ago, and we came out on top this year. I’m sure we’re going to have many future series.”

The Blues advanced to play Nashville in the second round, with Game 1 against the Predators at home in St. Louis.

“I think we should be proud, but not satisfied,” Paajarvi said, adding: “We’ve got to play a better game.”

Allen made 34 saves for the Blues, who led 2-0 and 3-1 before a furious rally by the Wild to try to keep their season alive forced the extra frame. Mikko Koivu and Jason Zucker scored to bring the Wild back from their second two-goal hole, a deficit that held past the midpoint of the third period until the two scores 4:21 apart that Allen said the Wild deserved for how hard they came at him.

Vladimir Tarasenko scored for the first time in the series, Alexander Steen followed him 3:15 later for a 2-0 lead midway through the first period and Paul Stastny got a goal in his first appearance of the playoffs, but the Blues were still fortunate to make it to overtime with all the difficult saves Allen had to make.

Despite a clear edge in shots on goal and faceoff draws and a dominant penalty kill unit throughout the series, the Wild were left wondering what more they had to do to get more pucks past Allen.

“They weren’t the better team,” coach Bruce Boudreau said, “but they won four games.”

Paajarvi’s first career playoff goal was set up by Wild goalie Devan Dubnyk, who stopped 23 shots. He turned the puck over to Vladimir Sobotka, whose pass found the trailing Paajarvi for the winner.

That gave Yeo the satisfaction of beating the team that fired him a little over a year ago, his insider knowledge of the Wild’s preferences and tendencies undoubtedly a strategical benefit for the Blues.

“I don’t think that what I’m feeling right now would be any different if it was any other team,” said Yeo, who was congratulated in the locker room afterward by Wild general manager Chuck Fletcher.

Ryan Suter scored the first of two power play goals by the Wild, who posted a 26-12 advantage in shots on goal over the second and third periods after weathering an early barrage by the Blues. They lacked that finishing touch to reward their 5-on-5 effort, though, and Dubnyk couldn’t quite match Allen’s brilliance.

The Wild also lost first line center Eric Staal to a scary injury in the second period when he crashed head first into the boards and, though alert and stable, was sent to a nearby hospital for further observation. Erik Haula filled in admirably, but in defeat.

“What is this, five years in a row? I’m sick of it,” Haula said. “We’re all sick of it.”

The Wild had a goal waved off earlier in the third period for goaltender interference on Nino Niederreiter. Coach Bruce Boudreau challenged, arguing that Jori Lehtera pushed Niederreiter into Allen, but the video review upheld the call to trigger an angry, dismissive wave of the left hand by Boudreau.

Tarasenko, who had six goals in six games against the Wild in the playoffs in 2015, used some fancy footwork to give the Blues the early lead. He charged in from the corner and, after a collision of sticks with Wild defenseman Jonas Brodin, kept the puck alive by pin-balling it off the inside of both skates before going to the opposite side to beat Dubnyk .

“It’s impossible to pick one thing,” Koivu said, “why we came up short like that.”

NOTES: The Wild fell to 1-7 in their last eight home games in the playoffs, with the only win coming in Game 3 against Dallas in the first round last year. … The Blues are 7-2 in their last nine postseason road games. … Koivu had his first goal in 22 games since March 7, which also came against the Blues. … Stastny missed the last 14 games because of a lower-body injury. He has eight goals in 20 career playoff games against Minnesota.