The Stars, who went to a shootout for the first time this season, got goals from Eaves and Jamie Benn. But Minnesota's Jason Pominville, Mikko Koivu and Chris Stewart scored on Stars goalie Kari Lehtonen, who stopped 31 of 33 shots in the game and 2-5 in the shootout.
The Stars, who fell to 1-3-2 over their past six games, are 19-20-10 on the season. They are 2-10 in games that have gone beyond regulation.
"We're playing OK hockey, but we're just not getting the results," said Benn. "It's still not good enough, especially where we're at, where we're sitting in the standings, we have to have two points every night. That's another tough one where we let a point slip away."
The Wild (31-11-5) ran their road points streak to 13 games (11-0-2) and improved to 20-3-1 in their past 24 games overall.
"It really doesn't matter how you get the win, as long as you're in the game," said Wild captain Mikko Koivu. "We will take it. It's never easy to win on the road, so we thought that was a good road game."
The Wild outshot the Stars 14-8 in the first period and scored the only goal when Pominville scored from the right circle on a two-on-one rush at the 13:35 mark.
Minnesota extended its lead to 2-0 by cashing in on its second power play of the game. After a nice entry by Mikael Granlund into the Dallas zone, Nino Niederreiter set up Koivu who scored off a one-timer from the right circle at 4:38 of the second.
The Stars cut the lead to one midway through the second. After Spezza forced a turnover in the Minnesota zone, Antoine Roussel backhanded the puck to Seguin who scored off a blast from the left circle to make it a 2-1 game at the 9:38 mark.
The Stars went on a 1:52 five-on-three power play with 40.8 seconds left in the period and scored to tie the game. A Benn pass bounced off traffic and Eaves batted the puck out of midair past Wild goalie Devan Dubnyk to make it a 2-2 game with 20.4 seconds left in the period.
Both teams had a power play chance in the third, but neither team cashed in. And that sent the game to overtime and then the shootout, where the Stars couldn't get the second point.
"It's definitely frustrating because I think we're playing an okay game," said Benn. "We're giving ourselves a chance to win these games and not coming out with the results."
Notes
\The Stars are 2-10 in games that have gone beyond regulation, including 2-9 in 3-on-3 overtime and 0-1 in shootouts.
\The Stars are 1-2-3 in their past six home games.
\Patrick Eaves scored his 18th goal of the season, which leads the team.
\Eaves is tied for second in the NHL with 10 power-play goals.
\The Stars outshot Minnesota 37-33 and had a 72-59 advantage in shot attempts.
\Jamie Benn led the Stars with 8 shot attempts.
\The Stars were 1-5 on the power play and 3-4 on the shootout.
\The Stars won 33 of 60 faceoffs (55 percent). Jason Spezz and Tyler Seguin both won 7 of 10 faceoffs.
*John Klingberg led the Stars with 27:46 of ice time.
What's Next
The Stars continue their homestand Thursday when they take on the Buffalo Sabres. This will be the final game before the All-Star break for the Stars. The Sabres won the first meeting between the two teams, defeating the Stars, 4-1, in Buffalo on Jan. 16.
Stars Lineup
Jamie Benn - Cody Eakin - Patrick Eaves
Antoine Roussel - Tyler Seguin - Jason Spezza
Lauri Korpikoski - Devin Shore - Patrick Sharp
Curtis McKenzie - Adam Cracknell - Brett Ritchie
Esa Lindell - John Klingberg
Dan Hamhuis - Jordie Benn
Patrik Nemeth - Stephen Johns
Kari Lehtonen
Antti Niemi
Scratched: Jiri Hudler, Julius Honka
Injured: Radek Faksa (lower body), Johnny Oduya (lower body), Jamie Oleksiak (hand), Ales Hemsky (hip), Mattias Janmark (knee)
This story was not subject to approval of the National Hockey League or Dallas Stars Hockey Club. Mark Stepneski is an independent writer whose posts on DallasStars.com reflect his own opinions and do not represent official statements from the Dallas Stars. You can follow Mark on Twitter @StarsInsideEdge.
