Denis Gurianov scored his fourth goal in six games for the Stars (30-19-5), who are 3-2-1 in that span. Bishop made 27 saves.
"Not good enough for this time of year against a team that's chasing you," Dallas forward Andrew Cogliano said. "They're a pretty solid team in terms of coming off of a back-to-back (2-3-1 in second game). I thought they got better as the game went on."
Joe Pavelski scored on the power play at 15:28 of the first period to give the Stars a 1-0 lead.
Dallas outshot Minnesota 16-12 in the first.
"The power play got a big goal for us, and on the second one, they were moving the puck really well," Stars coach Rick Bowness said about their two goals. "We had more good looks in that first period than we've had in a long time, we just didn't put the puck in the net at the right times. Give their goalie credit."
Gurianov made it 2-0 with a one-timer from the right circle at 2:51 of the second, one second after a tripping penalty against Eriksson Ek expired. It was his 15th goal of the season, tying him with Roope Hintz and Alexander Radulov for the Stars lead.
"I saw [Wild forward Jordan Greenway fall while defending Miro Heiskanen] and I was waiting for him," Gurianov said. "Great job by Miro to pass me the puck, and I shot it."
Eriksson Ek got the Wild within 2-1 at 8:25 of the second when the puck went in off his skate near the right post.
"He's grown and matured," Minnesota coach Bruce Boudreau said. "Last year, he got a lot more responsibility in the last half of the year. This year, he's continued to not only gain more responsibility, but want and accept it."
Ryan Donato tied the game 2-2 when he scored from the bottom of the right circle at 12:09 of the second.
"These are important points for us," Eriksson Ek said. "We have to put more games together and keep winning, and this was a step in the right direction."
Radek Faksa had a chance to put the Stars ahead with a shot from the slot on the power play in the third period, but Dubnyk moved across the crease and made the save with his blocker.
"It was such a big game for him, and he deserved it," Boudreau said of Dubnyk, who earned his second win in five starts since Jan. 12. "He saved our bacon with about four minutes to go when they were on the power play and made a tremendous save. Hopefully, that's the start of something good for him."