The Wild are an NHL-best 11-1-1 since the All-Star break, outscoring the opposition 40-18 during that stretch to get into playoff position for the first time since Nov. 24.
Mikko Koivu, Stephane Veilleux, Matt Dumba and Mikael Granlund also had goals for the Wild during the highest-scoring period in franchise history.
Making his 17th straight start since being acquired from Arizona in mid-January, Devan Dubnyk finished with 18 saves to improve to 13-2-1 with Minnesota.
Jason Spezza scored twice for Dallas, which is 0-2-1 in its last three.
It was only the second time in 27 games this season that the Stars lost in regulation when leading after two periods (21-2-4).
Parise tied the score 1-all 100 seconds into the third period.
From the left point, Christian Folin skated along the boards until he was below the left circle. From there he backhanded a pass across the crease to Parise, who redirected the puck into the Dallas net.
Less than two minutes later, Koivu gave the Wild a 2-1 lead.
Off a Dallas turnover, he controlled the puck in the left circle and his bad-angle shot from below the circle eluded Jhonas Enroth. It was Koivu's second goal in three games.
Veilleux scored his first of the season midway through the period, fighting off a check in front to put home a rebound of a shot from Marco Scandella. Dumba scored on the power play at 13:25, and Granlund scored at 14:33.
Parise and Spezza scored 25 seconds apart late in the period.
Spezza made it 1-0 Dallas with a power-play goal at 14:33 of the second. He took the puck from below the Wild goal line and skated up the right wall. Instead of passing, Spezza pivoted at the half boards and skated to the right dot, beating Dubnyk high on the glove side with a slap shot for his fourth goal in eight games.
It was the first goal allowed by the Wild while short-handed since the All-Star break, a streak of 32 straight penalty kills.
NOTES: The division rivals do not meet again. Minnesota won the season series 4-1-0. ... It was Enroth's second start since being acquired from Buffalo on Feb. 11. He allowed four goals in a 4-1 loss to Colorado on Feb. 14. ... Wild D Jared Spurgeon missed his second straight game with an upper-body injury. He was hit in the face with a puck Wednesday. ... Dallas plays at Winnipeg on Tuesday. Minnesota is home against Edmonton that night.