Linemates Mike Ribeiro and Eriksson assisted on both of Ott's goals to help the Stars win their second straight at home after they matched a franchise record for futility with six consecutive home defeats.
The Ott-Ribeiro-Eriksson line has been on a recent tear, combining for 24 points in the last six games, seven points against Minnesota.
"We knew it was going to be a very tight game and we talked about finding ways to win," Stars coach Dave Tippett said. "That line certainly took it to heart."
Dallas and Minnesota are among seven teams battling for the final two Western Conference playoff spots.
"Right now this is the playoffs," Ott said. "Every single night is a fight for that playoff spot."
The Stars have 74 points, two more than the Wild, who earned a point with the overtime loss after erasing a two-goal deficit with a second-period rally.
"To get a point after they got a 2-0 lead is huge, especially at this time of year," Minnesota coach Jacques Lemaire said.
Minnesota has lost three in a row, but all three have been in overtime or a shootout, meaning the Wild is still picking up points.
Each team had prime scoring chances in the third period. Dallas' James Neal hit the post with a rebound 1:11 into the third period, and Turco stopped Minnesota's Peter Olevcky from point-blank range with 14:20 left in regulation.
Backstrom made a sharp glove save on Ott's drive from the right circle with 3:49 to play in regulation.
Backstrom denied Dallas' Mike Modano from the right circle with under 4 minutes left in overtime, and smothered Brendan Morrison's deflection with 2:52 remaining in the extra session.
Dallas is 15-3-1 in its last 19 meetings with Minnesota.
The Stars got an early jump when Ott scored off Eriksson's pass through the crease 2 minutes into the opening period.
Ott converted Ribeiro's cross-ice pass 38 seconds into the second period for a 2-0 lead.
"I give Otter a ton of credit," Tippett said. "He's taken his game to another level. He has an impact on every game we play."
Koivu connected from the slot 18 seconds into a power play at 12:09 of the second period to pull Minnesota to 2-1, and 1:51 later Brunette's deflection tied it.
"It's a big point," Minnesota's Pierre-Marc Bouchard said. "We stuck together and we showed some character. We started creating and taking shots and got some energy."
Eriksson's three assists were a career high. ... Ribeiro has points in seven straight games, matching his career high. ... Turco has started 39 of the last 40 games. ... Minnesota RW Marian Gaborik is practicing for the first time since sustaining a hip injury in December, but there's no timetable for his return. Injuries have limited Gaborik to six games this season. ... LW Derek Boogaard was back for the Wild after missing Thursday night's 2-1 shootout loss at Colorado because of an illness. ... Stars RW Jere Lehtinen (upper body) and LW Fabian Brunnstrom (shoulder) were among the scratches, but are close to returning.
Copyright by STATS LLC and The Associated Press
Arena: American Airlines Center Location: Dallas, Texas
Referees: Bill McCreary, Mike Hasenfratz Linesmen: Mike Cvik, Don Henderson
Attendance: 18,584 (100.3% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Steve Ott (14)
Assists: Loui Eriksson, Mike Ribeiro
Steve Ott (15)
Assists: Mike Ribeiro, Loui Eriksson
Mikko Koivu (18)
(Power Play) Assists: Antti Miettinen, Andrew Brunette
Andrew Brunette (16)
Assists: Nick Schultz, Pierre-Marc Bouchard