Newcomer Franco Fragapane scored for Minnesota, which has settled for a draw in its past two matches after winning two in a row. Minnesota is 0-2-2 on the road this season while earning its first-ever point in five matches in Dallas (0-4-1).
Dallas remains undefeated at home this season.
Minnesota was in control in the first half, getting five of their eight shots on goal while limiting Dallas to one on goal on just three attempts.
Fragapane put Minnesota ahead 1-0 in the 36th minute, kicking in a rebound in his MLS debut. Jacori Hayes drove down the right wing before sending a cross to Adrien Hunou, whose shot from the middle was saved by goalkeeper Jimmy Maurer. Maurer couldn't stop the rebound, which bounced out to Fragapane on the left side.
Dallas came out firing early in the second half.
Ricardo Pepi's shot from the right side at the top of the box reached the net but Tyler Miller deflected it wide in the 47th minute and then moments later midfielder Bryan Acosta missed a chance for the equalizer by inches when his shot went just over the crossbar.
Dallas finally broke through in the 68th minute. Pepi found space along the backline and sent a shot to the bottom left corner past Miller to even the score 1-1.
The two sides exchanged chances through the rest of the second half. Dallas midfielder Facundo Quignon and forward Franco Jara saw their shots sail over the net in the 79th and 80th minutes, respectively. Minnesota came back in the following minutes, with Emanuel Reynoso's chance going just wide right of the net while Maurer got a piece of Ethan Finlay's shot from the right to deflect it over the net.
Reynoso had another glorious opportunity in the final minute off a pass from Ethan Finlay but couldn't finish to secure the three points.