The Stars became the first team in NHL history to score in the first 1:15 in four consecutive games when Robertson gave them a 1-0 lead at 1:08 of the first period.
Boone Jenner tied it 1-1 on a breakaway at 6:53, and Alexandre Texier gave Columbus a 2-1 lead on a wrist shot that beat Oettinger stick side at 1:25 of the second period.
"When things are not going that well, you try to keep it simple," Columbus forward Alexandre Texier said. "I thought we tried to keep it (simple) as a team, and I try to do that too. But at the end we care about the result, so we have to learn and move on."
It was the first time the Stars trailed in five games, but Tyler Seguin tied it 2-2 when he redirected Hakanpaa's point shot at 16:25.
"Just got back to our style, which is our forecheck," Seguin said. "We all know how we defend. Started winning a lot more puck battles and started competing, and really had a five-man unit out there. Once that happened, I thought the game was ours."
Robertson gave Dallas a 3-2 lead than a minute later when he scored five-hole at 17:14. Pavelski carried the puck through the neutral zone, then worked his way past forward Sean Kuraly near the Blue Jackets blue line before passing to Robertson in the left circle.
"I immediately think it's a 2-on-1 when he does that," Robertson said of Pavelski. "But then you look on the replay and it's like, 'Wow, he dipsy-doodled the one guy.' It's like, 'That's impressive Joe, I didn't expect that to be honest.' Then he made a great play."
The Blue Jackets were outshot 31-11 over the final two periods.
"They're a big-bodied team, they get rolling and they do a really good job of getting to the net," Columbus coach Brad Larsen said. "You've got to be boxing out, you've got to do a real good job there. We got chasing a little bit there. I thought the first period, like I said, they had two chances in the first minute, minute and a bit, and they didn't have anything the rest of the period.
"They're at home, they've been playing well. They're going to get a response, and they came. It's a veteran team. They've got four lines with good size, they started to come. We had to weather their storm there."
NOTES: Stars defenseman John Klingberg was a late scratch because of an illness that is not COVID-19 related. Bowness said he expects Klingberg to play Monday against the Arizona Coyotes. … Dallas defenseman Esa Lindell led all skaters with 30:28 of ice time. He had four shots on goal, three hits and two blocked shots. … Pavelski is the first NHL player 37 or older to have four straight multipoint games since Cliff Ronning with the New York Islanders in 2003-04. He has scored nine points (three goals, six assists) in his past four games. … Merzlikins was well enough to dress as the Blue Jackets backup goalie. … Columbus has been outscored 15-5 on the road trip.