Talbot, whose wife is scheduled to give birth to twins in the morning, bounced back from a 6-2 loss against Buffalo on Sunday.
"I tried to leave that at home for the three hours I was here," said Talbot. "I knew I had a job to do tonight before that. I knew I'd feel much better tomorrow morning going in there with two points. That was my focus coming to the rink tonight."
Slepyshev sniped a shot from the top of the circle to put the Oilers up 1-0 at 1:51 of the first period. Slepyshev's tally was his first in the NHL. Leon Draisaitl recorded the lone assist.
Eberle made it a 2-0 game with an interesting play at 9:22 of the first. The Oilers winger tried to centre a puck in front to Milan Lucic, but it deflected in off of Hurricanes defenceman Ron Hainsey instead. The goal was Eberle's third of the season in four games, tying Connor McDavid for the team lead.
"I was trying to find Lucic in the slot," said Eberle. "I was laughing because if it would have went through to him then it would have been an A chance too. You get bounces like that and it's nice. It was a good cycling shift. For the whole time, we kind of hemmed them in then finally got it to the net."
Oilers defenceman Mark Fayne, playing in his first game of the season, was injured in the opening period and did not return for the second.
It took Edmonton 2:35 into the second to increase their lead to three. Off an offensive zone draw, Pitlick placed a shot over the shoulder of Ward for a 3-0 lead and his second goal of the season. Pitlick was assisted by Mark Letestu and Anton Lander.
The Hurricanes came into the night coming off two straight losses to open their season. In both losses, they had three-goal leads but their opponent came back to win. Tonight, Carolina found themselves the ones down 3-0. They were able to rally to make a game of it.
Talbot's shutout bid ended at 3:18 of the third. Lee Stempniak buried a rebound opportunity to make it 3-1. Stempniak was assisted by Victor Rask and Justin Faulk.
Video: POST-GAME RAW | Cam TalbotJeff Skinner set up Stempniak with a centring pass out in front for his second of the night and team-leading third of the season, at 4:14 of the final frame. Oilers Head Coach Todd McLellan challenged that the play was offside but failed to have the call reversed. Stempniak's second put Carolina back by just one.
"We knew they were going to come out hard in the third period," said Eberle. They pushed it and got a couple goals there. But I liked the way our group, after the second one, started to pick up our game a bit, play in their end a little more and weather the storm.
"Any time you're up three goals, sometimes the game gets into a bit of a lull. Then the losing team picks up. We've been on the other end of it too where you start getting a ton of shots and feel like you're going to come back. I liked the way we weathered the storm. At the end of the day, Cam was great and got us the win."
The elusive third goal wouldn't come for Carolina as Talbot shut the door the rest of the way. One of his biggest saves came with 2.3 seconds left when he flashed the glove to deny Jordan Staal the tying goal.
"Personally, I obviously needed a big bounce-back game after the game I had last time," said Talbot. "As a team, I think we sometimes let those losses snowball in the past. Tonight we came out hard. We talked about being a tough, resilient group and a bounce-back group and that's what we came out with tonight."
The Oilers host the St. Louis Blues Thursday, at 7 p.m. MT.