McElhinney made 44 saves and Alexander Wennberg scored the shootout winner on Wednesday as the Columbus Blue Jackets edged the Edmonton Oilers 4-3.
David Savard, Ryan Johansen and Mark Letestu scored in regulation for the Blue Jackets (31-35-4), who have won four of their last five.
"We put ourselves in some situations that we wouldn't have liked to be in, but for the most part, we found a way to squeak it out," McElhinney said. "I think the main thing was keeping it a one-goal game when we got down to 3-2. We were trying to keep it tight. (Letestu's) goal was great. It was tough generating shots for us, so to get a goal from that line at that time, was huge."
Letestu credited his goalie for keeping the Jackets in the game.
"They took it to us most of the night," he said. "Mac stole this one for us and sometimes your goalie has to be big like that."
Derek Roy, Ryan Nugent-Hopkins and Nail Yakupov responded for the Oilers (19-39-13), who have lost eight of their last nine games.
"We played well, we had our opportunities to finish them off and put the puck in the net and we didn't capitalize," said Oilers forward Jordan Eberle. "You have to give their goalie credit, he played well. And when you get to a shootout it's anybody's game."
Columbus started the scoring 5:30 into the first period on their first shot of the game as defenceman Savard used a screen on a 4-on-4 to beat Oilers goalie Ben Scrivens top corner.
Edmonton outshot Columbus 14-4 in the first, its best chance coming when Yakupov rang a power-play shot off a post behind McElhinney.
Johansen cleanly beat Scrivens on a wrist shot from the top of the right circle to give Columbus a 2-0 lead four minutes into the second.
The Oilers got on the board 11 minutes into the second period on the power play as Benoit Pouliot made a long pass to spot Roy wide open at the side of the net for his 10th of the season.
Eberle danced his way in tight before dishing it off to Nugent-Hopkins, who hit the 20-goal mark for the first time in his career as Edmonton tied the game 2-2 just 1:28 into the third period.
"Going into this season I wanted to get over 20," Nugent-Hopkins said. "I am feeling pretty good this year. I am happy with that accomplishment.
The Oilers took a 3-2 lead midway through the third as an Oscar Klefbom shot came off the boards to Yakupov on the other side and he deposited his 12th of the season into the net.
Letestu responded for the Blue Jackets 54 seconds later, ripping a long shot off the post and in past Scrivens.
Edmonton outshot Columbus 47-20.
The Blue Jackets play the second game of a three-game trip in Vancouver on Thursday. The Oilers remain at home to face the Philadelphia Flyers on Saturday.
Notes: Columbus won the only other meeting between the teams this season 5-4 in a shutout last Friday… Blue Jacket forward Artem Anisimov played his 400th career NHL game… Forward Andrew Miller made his NHL debut for the Oilers in the contest… Edmonton defenceman Nikita Nikitin played for the first time since sustaining a shoulder injury on Jan. 29.