The defending Western Conference champion Stars, who are in sixth place in the Central Division, went ahead for good when Jason Dickinson assisted on goals by Gurianov and Heiskanen just more than a minute apart late in the second period for a 2-1 lead.
Gurianov scored again with just under 12 minutes left in the game on a shot from the left side parallel to the front of the net that ricocheted off Blue Jackets defenseman Michael Del Zotto into the net. Pavelski scored his team-leading 17th goal about seven minutes later.
The Stars won on a night when Nashville and Chicago, the teams directly ahead of them in the standings, both lost.
The Blue Jackets and Stars wrap up their regular-season series on Saturday night, with Dallas holding a 4-2-1 series lead.
Jack Roslovic scored on Columbus' first shot, taking a pass from Del Zotto and pushing the puck through a wide-open gap to the net behind rookie Jake Oettinger's extended left leg. The Blue Jackets have lost four in a row and seven of eight.
Oettinger, playing for the first time in five games, stopped the final 17 shots he faced.
Dallas, which has 44 points with 14 regular-season games left, was coming off consecutive overtime losses. One of those was at the fourth-place Predators, who hold the division's final playoff spot with 49 points and 11 regular-season games to play. The fifth-place Blackhawks have 45 points with 12 games to play.
Blue Jackets goalie Elvis Merzlikins had some close calls even before Gurianov and Heiskanen scored 79 seconds apart to make it 2-1 at the second intermission. Merzlikins had 27 saves.
Gurianov's initial goal came when he knocked in his own rebound past a sprawling Merzlikins to tie it at 1 with 3:18 left in the second period. Heiskanen scored, including an assist from Gurianov, on a shot from the slot that went under the goalie's right arm.
PUCK TO THE FACE
Six-time All-Star center Tyler Seguin, still rehabbing from offseason hip surgery, went through the morning skate with the Stars. Coach Rick Bowness said it was a positive step for Seguin, who looked good on the ice. Stars general manager Jim Nill said Monday that Seguin could debut in about two weeks, which could be April 26 at home against Carolina.