SAINT PAUL, Minn. -- For the Dallas Stars, the drama and the highs and lows, if they result in a playoff series win, are all part of the process.

Dallas built a big lead Sunday afternoon and needed all of it to clinch its first-round playoff series with the Minnesota Wild.

First-period goals by John Klingberg, Jason Spezza and Patrick Sharp gave Dallas a commanding lead and helped withstand a furious Minnesota comeback, as the Stars beat the Wild 5-4, winning their best-of-seven series 4-2 and advancing to the second round.

Goalie Kari Lehtonen had 25 saves while Jamie Benn and Alex Goligoski added later goals as the Stars advanced past Round 1 for the first time since 2008.

"You have to win a series, and we found a way to win it," Stars coach Lindy Ruff said. "I thought the Wild played one heck of a series. There wasn't any quit in them. They came hard with five guys when they were down, they got a little life in this building and they made it tough."

Minnesota got 19 saves from goalie Devan Dubnyk, a pair of goals from defensemen Jared Spurgeon and single goals from Jonas Brodin and Jason Pominville, making a spirited late charge after trailing 4-0.

"It was fun. It was a blast. But we didn't get the job done," said Wild interim head coach John Torchetti, who faces an uncertain future. "We can't be happy walking away, that's for sure. We should be playing, and it makes it tough for the summer."

Back-to-back penalties against the Wild gave Dallas more than a minute of a 5-on-3 power play. Dubnyk made a pair of highlight-reel saves, but Klingberg finally got the Stars on the board with a slap shot from the left circle after a cross-ice pass from Spezza. It was Klingberg's first goal of the playoffs, but his name is familiar to the Wild. In the regular season, Klingberg had a pair of overtime-winning goals versus Minnesota.

The Stars went up 2-0 before the first period was half over when Dubnyk stopped, but couldn't cover, a shot from the blue line. While the goalie was looking for the loose puck, Mattias Janmark got it to Spezza at the left of the net, and Spezza's backhand shot doubled the Dallas lead.

It was 3-0 after a period thanks to a seeing-eye wrist shot by Sharp with less than two minutes left in the first. Coming in on a 2-on-1 break, Sharp let Jamie Benn break toward the net, then launched a rising shot headed for Dubnyk's blocker side. The goalie lunged at it a split second too late, giving Sharp his third goal of the playoffs.

Content to defend their commanding lead and play defense, the Stars had just five shots on Dubnyk in the second period, but the fifth one was significant. With less than 24 seconds to play in the period, Benn snapped off a wrist shot that fooled Dubnyk on the glove side, making it 4-0 and producing a notable round of boos from the Minnesota crowd.

"Very big power play goal to get us started and a 4-0 lead. What else can you ask for?" Sharp said. "A lot of things that you can take out of this that are good, a few things that are bad, but it's never easy to win a playoff series, especially against a tough team like Minnesota."

The Wild fans finally got a reason to cheer in the third period when Spurgeon scored a power-play goal, shoveling in the rebound of a Mikael Granlund shot that Lehtonen had stopped. Just 16 seconds later, Brodin scored on a backhander from low in the right circle after a shot by Erik Haula was blocked in front of the net, but went right to Brodin.

"The building got loud. Probably one of the most useless timeouts I've taken, because they couldn't hear a word I said anyway," Ruff said. "But I was just trying to tell them, 'Listen, we've got to play.' You've got to live that environment to get better at it."

When Spurgeon scored another power-play goal at the 8:39 mark, cutting the Dallas lead to 4-3, the crowd was deafening, but Gologoski dropped the decibel level considerably. His shot from the blue line hit Dubnyk and landed at the goalie's feet. Unaware that the puck was under him, Dubnyk dropped down and inadvertently knocked the puck into the net.

Pominville's goal came with less than five minutes to play, pulling Minnesota back within a goal. The Wild pulled Dubnyk for the final two minutes. A shot by Nino Niederreiter with 33.9 seconds left had the Wild thinking they had tied the game. A review showed the puck just on, but not over, the goal line before it was covered by a Dallas defenseman.

"It's a shame we didn't come out like that," said Wild center Charlie Coyle of the frantic third-period push. "Tough first couple goals put us behind. But for us to battle back like that, it was a good feeling. It was right there and we felt it. It comes down to inches there and we just couldn't get it."

The Stars, who were the top seed in the West, will host either Chicago or St. Louis to open Round 2.

NOTES: In the wake of renowned Minnesota musician Prince's death last week, the Wild had a playoff towel draped on each of Xcel Energy Center's 19,000-plus seats, and behind the team bench had the towels arranged to form the symbol Prince used as a brand in the 1990s. The Wild also held a moment of silence in Prince's memory before the game. ... For the fifth time in the six games of this series, Stars C Tyler Seguin was scratched from the lineup due to a lower-body injury. He played in Game 2 in Dallas but has not been along on either of his team's trips to Minnesota. ... The Stars attempted 93 shots on goal in Game 5 in Dallas, and got 41 of them on net. But Minnesota's 34 blocked shots in the game were a franchise record. The Wild led the NHL with 118 blocked shots in the playoffs after the first five games.