Justin Faulk scored twice and Dylan Larkin had a goal and an assist for the Red Wings (40-29-9), who have lost seven of their past nine games, including five straight at home. Gibson made 32 saves.
“That’s a disappointing finish, and I hope that’s not the one,” Larkin said. “I don’t want that game to be the final nail in the coffin.”
Detroit is tied with the New York Islanders, three points behind Ottawa and one behind Columbus for the second wild card.
“I liked our effort, and we got a point,” Red Wings coach Todd McLellan said. “That point might keep us alive. We are in must-win territory here, but we are still in it.”
The Blue Jackets took a 1-0 lead at 2:06 of the first period. Axel Sandin-Pellikka turned over the puck behind the Detroit net and Mason Marchment fed Heinen in front for his sixth goal of the season.
Larkin made it 1-1 with a power-play goal at 10:27. Erik Gudbranson blocked Larkin’s attempted pass to Alex DeBrincat at the back door, but Larkin was able to sweep in the loose puck for his 31st goal.
Faulk, who missed the previous two games with a lower-body injury, gave the Red Wings a 2-1 lead at 6:27 of the second period, splitting the defense and putting the puck over Greaves’ glove for his 13th goal.
Werenski made it 2-2 with a power-play goal at 10:59, beating Gibson with a long wrist shot over his right shoulder. Greaves got the secondary assist for his first NHL point.