The Oilers' last three victories came in the shootout, as did six of their previous nine wins this season.
"It was a good feeling to get one in regulation," Edmonton coach Craig MacTavish said. "We're not doing anything the easy way. It would have been nice to win a couple games at the beginning of the homestand and gives ourselves a chance to put something together. But it was nice to recover and get to .500 during this stretch."
Cogliano, a rookie who picked up his fifth goal of the season and 14th point, said getting a victory inside of 60 minutes was big for the team's confidence.
"It was a solid team effort," he said. "To get a regulation win and go on the road with two wins under our belt is big for our team. Overall, I thought we played pretty well on the homestand. As of now we are pretty confident."
The Oilers improved to 10-13-1 and moved five points behind first-place Minnesota and two behind fourth-place Calgary in the Northwest Division.
Ron Hainsey scored for Columbus, which snapped a two-game winning streak in the opener of a three-game road trip. The Blue Jackets remained tied with Chicago and St. Louis for second place in the Central, six points behind Detroit.
Columbus forward Jason Chimera said his team should have been able to get back into the game when they were given a late 5-on-3 advantage.
"We blew it on the power play at the end," he said. "We had a great chance there at the end and didn't take advantage of it. You work hard to get that 5-on-3 and then you have to make sure you get something out of it. We outplayed them for the most part but couldn't get people in front of the net."
The Oilers took the lead just 3½ minutes into the game as Brodziak's wrist shot seemed to handcuff Columbus goalie Pascal Leclaire and dribbled off his glove and behind him into the net.
The Blue Jackets had a chance to tie the game just past the 14-minute mark as Rick Nash was awarded a penalty shot after being hauled down on a power-play breakaway opportunity by Oilers defenseman Ladislav Smid. However, Nash's attempt to pick the top corner sailed wide.
It didn't take the Blue Jackets long to make up for the miss as they struck off the faceoff just six seconds later. Hainsey's point shot beat Roloson low to the stick side at 14:10.
Columbus lost Leclaire for the remainder of the game six minutes into the second as he tweaked a hamstring muscle and was replaced by backup Fredrik Norrena.
"That was tough," Nash said. "He's the backbone of our team. Freddy came in and played well. Hopefully (Pascal) is all right."
The Oilers looked to have beaten Norrena with fuve minutes remaining in the middle period when Cogliano went in on a short-handed breakaway and his shot bounced behind the Columbus goalie, only to be swatted away in the nick of time by Hainsey. After a video review, the original call stood and the game remained tied heading into the third period.
Cogliano took advantage of another chance midway through the third, swatting a pass from Robert Nilsson into the crease past Norrena to make it 2-1.
The Oilers got themselves into penalty trouble late in the game, allowing the two-man Columbus power play, but Edmonton killed both as Roloson stood his ground.
Hemsky scored an empty-netter with 16 seconds left to seal the win.
- The Oilers were without D Dick Tarnstrom, who suffered a concussion in Saturday's win over Chicago.
- Edmonton D Mathieu Roy could be back with the team soon. The Oilers have sent him on a two-week conditioning stint to Springfield of the AHL as he recovers from a shoulder injury.
- Also, RW Fernando Pisani could be back with the Oilers as early as next week. Pisani is well ahead of expectations and regaining his strength quickly after losing 30 pounds due to colitis.
- Nash's point-scoring streak ended at six games.