Artem Anisimov and Mark Letestu added first-period goals to the one Columbus already had when the puck dropped in a makeup game with Dallas, and the Blue Jackets withstood a frantic third period for a 3-1 victory over the equally playoff-hungry Stars.
"It's been a long time," said winger Jared Boll, one of the few players remaining from the Blue Jackets' last playoff team in 2008-09. "It's just the first step. We've still got a long way to go."
The Blue Jackets had a 1-0 lead when the puck dropped because that was the score March 10, the night the original game was postponed after Dallas forward Rich Peverley collapsed on the bench because of an irregular heartbeat.
Anisimov doubled the margin on an unassisted goal just 1:33 into the game. That was 71 seconds faster than the goal last month by Nathan Horton, who got credit for it even though he didn't officially play because he missed the makeup game with a lower-body injury.
"The only thing that was weird about it was looking up at the scoreboard in warm-ups and we had a 1-0 lead," Columbus coach Todd Richards said. "But once you got into the game, I had to remind myself when we scored the first goal that we were up 2-0, not just 1-0."
The Blue Jackets set a franchise record with 42 wins, beating the previous mark from their only other playoff season.
Columbus was swept by Detroit in the first round five years ago, and now those teams are in a battle for playoff position in their first season since being moved to the Eastern Conference.
"It's fun right now to say we clinched, but we can't be satisfied with just getting in," said Boll, who missed four months with a torn ankle tendon. "We want to get there and make a splash."
The Stars, who are in a franchise-record playoff drought that's a year longer than what Columbus endured, never really gave themselves a chance to build a cushion on Phoenix for the final playoff berth in the West.
Dallas (89 points) has a two-point lead over the Coyotes, who have three games left to two for the Stars.
"We fell behind before the game even started," Dallas forward Jamie Benn said. "That didn't help, but we're not making any excuses."
Dallas trailed 3-0 after the first and couldn't capitalize on power plays with fresh ice at the start of the second and third periods against Columbus goalie Sergei Bobrovsky, who stopped 17 of 18 shots in the third period and 33 of 34 overall.
The Russian had to work harder at the start of the third, stopping Tyler Seguin on a backhand shot in the crease after Dallas' leading scorer skated around the defense and turning away Benn from the wing a few seconds later.
The Stars scored when they pulled goalie Tim Thomas for a 6-on-4 power play with nearly 14 minutes left in the game. Bobrovsky made a sprawling save before Trevor Daley punched in a rebound in a crowd in front of the net.
"I broke my old record by a couple of minutes," Stars coach Lindy Ruff said. "I pulled a goalie one time in Atlanta with 9-something. I pulled it at even strength and we didn't score, but we scored the next shift and we pulled him late in the game and ended up tying it, and won it in overtime."
Dallas outshot Columbus 18-2 in the third period, when the Stars went with an empty net for a total of about 5 minutes.
The Stars ended up playing four times in five nights because of the makeup game, the same thing the Blue Jackets are doing to finish the season. Columbus was on the second night of a back-to-back and is the first team to play on four of the last five days of the season since Ottawa in 1993.
Because of the busy schedule, Dallas coach Lindy Ruff went with Thomas over Kari Lehtonen.
Thomas was fooled by Anisimov for the Columbus center's third goal in two games against the Stars, and Letestu made it 3-0 when his shot went off Daley's stick to the side of Thomas and somehow slid between the goalie's legs.
NOTES: STATS research going back to the 1989-90 season couldn't find an instance where a player scored a goal without officially playing in a game. Matt Calvert and James Wisniewski got credit for assists on Horton's goal. ... Daley tied his career high from three years ago with his eighth goal.