Gurianov ended a 10-game goal drought, and Miro Heiskanen scored 1:19 later in the second period for the Stars (16-14-12), who extended their point streak to five games (3-0-2). Jake Oettinger made 17 saves.
"It feels good," Gurianov said. "We won the game and we got two points. Important points for us. We're playing for the playoffs. It felt good to score two goals and help my team to win."
Elvis Merzlikins made 27 saves for the Blue Jackets (15-21-9), who have lost four in a row and 11 of 13.
The teams will play again in Dallas on Saturday.
"We made some plays that we hurt ourselves," Columbus coach John Tortorella said. "For the life of me, we don't understand situational play. It is so frustrating to me that we don't grasp situational play."
The Stars are in sixth place in the eight-team Discover Central Division but moved within five points of the fourth-place Nashville Predators, who lost 4-1 at the Carolina Hurricanes on Thursday. Dallas has played three fewer games than Nashville. The Blue Jackets are seventh in the Central, 10 points behind the Predators. The top four teams will qualify for the Stanley Cup Playoffs.
Jack Roslovic gave Columbus a 1-0 lead on its first shot on goal at 7:16 of the first period. He gathered a turnover in the neutral zone and completed the rush with a tap-in off a pass from Michael Del Zotto skating down the slot.