The Blue Jackets almost tied it 1-1 1:00 into the third period during a power play when a shot by Marcus Bjork was tipped by Jack Roslovic off the right post.
Nyquist hit the left post at 17:23.
"I gave it a little early celebration there," Nyquist said. "I thought it was in."
Robertson ended a seven-game drought, scoring his 24th goal into an empty net at 18:53 to make it 2-0.
Johnson scored with 15 seconds left for the 2-1 final. The rookie forward has seven goals.
"I thought the first period was a little loose," Stars coach Pete DeBoer said. "I thought in the second and third we tightened up defensively. We just couldn't extend the lead to really put them in a hole. Got to give them credit for hanging around to the end.
"Every time you win a game like this, you learn some things and guys get put in situations. I liked our patience. … We didn't extend ourselves looking for the second goal."
Tarasov made his third straight start with Joonas Korpisalo out with a lower-body injury the past five games and Elvis Merzlikins struggling (4-8-0, 4.68 goals-against average, .864 save percentage).
"Most goalies want to get into a rhythm if they can," Blue Jackets coach Brad Larsen said. "That was a big reason I wanted to see him. He looked very comfortable tonight. Every time you see him in there, he does look more comfortable."
Tarasov made 26 saves in the first two periods.
"I'm trying to do my best to help with the guys," he said. "Sometimes it doesn't happen, so I just keep working on it."
NOTES: Columbus forward Yegor Chinakhov did not return after sustaining a lower-body injury 1:20 into the first period when Dallas forward Joel Kiviranta fell on the back of his left knee. Larsen had no update. … Oettinger, who turned 24 Sunday, played his 100th NHL game. He is 54-27-11, the second-most wins in his first 100 games in Stars/Minnesota North Stars history behind Ed Belfour (60). … Six of Johnston's eight goals have come on the road, trailing only Seattle Kraken forward Matty Beniers (7) among rookies. … Stars forward Riley Tufte had one shot and two hits in 12:04 in his season debut after being recalled from Texas of the American Hockey League on Dec. 12. … Blue Jackets forward Josh Dunne played 4:36 in his first NHL game since April 25, 2021. He was recalled from Cleveland of the AHL on Monday to replace Boone Jenner, who will have thumb surgery Tuesday and is expected to be out four weeks. … Columbus forward Carson Meyer had three shots and three hits in 12:08 in place of Cole Sillinger, who is day to day with an upper-body injury.