Jordan Eberle led the way with a goal and an assist in the Oilers' 3-2 victory over the Predators on Sunday.
"We had to decide after that game what kind of season this was going to be," Oilers coach Ralph Krueger said.
"Ever since we followed up that loss with a win in Chicago there has been a different swagger in the group. A different belief. I'm pleased it paid off with the two points tonight.
"These are huge points and it is a big step. We had a shot at catching Nashville nine days ago and they beat us 6-0. We had a shot at catching them again tonight and we were able to do it. It's a good time for that to happen."
Edmonton moved from 14th into a tie for 10th in the Western Conference, two points back of eighth-place San Jose.
Eberle admitted that having something to play for at this time of year is a bit of a novelty for the Oilers, who finished in 29th place last season after consecutive seasons in last place.
"When you get confidence it just builds and builds and builds," he said. "It's fun right now. It's March and we are two points out of a playoff spot. I haven't been in this situation before. It's exciting to be in the locker-room when every game and every period means so much. It's great to be a part of that."
"We're not finding the way to win games right now," Weber said. "We're giving games away. We are making mistakes. It's hard to comprehend right now. We need to get things back on track."
Edmonton's best opportunity in the opening period came midway through as Eberle stole a puck deep in the Nashville zone for a breakaway, but wasn't able to get Predators goalie Pekka Rinne to bite on his deke attempt, the Oilers' first shot of the game.
Nashville came close again with a minute left in the first period as it blazed in on a 3-on-1, only to see Josi's shot ring off the post.
The Oilers broke the deadlock eight minutes into the second period when Eberle was able to flick the rebound from a power-play point shot to Paajarvi, who hooked it into a wide-open net to make it 1-0.
The Predators tied the game on a power play with just over three minutes to play in the second period as Weber blasted a point shot past Dubnyk for his fifth of the season.
The Oilers took a 2-1 lead with nine minutes remaining in the third on a short-handed goal, as Sam Gagner won a race to a lost puck to create a two-on-one, dishing the pass off to Petrell, who beat Rinne with a quick one-timer.
Nashville's Sergei Kostitsyn was guilty of heading off to change on the play, creating the odd-man opportunity.
"I can't give you a logical explanation for an illogical event," Predators head coach Barry Trotz said. "He didn't recognize the situation."
Edmonton got an insurance goal with four minutes left as Eberle was able to beat Rinne with a high shot from the top of the circle to make it 3-1.
The Predators pulled Rinne and were able to get a goal from Josi with 8.4 seconds left, but the clock ran out on them from there.
The Predators wrap up a four-game trip on Tuesday in Columbus. The Oilers next play host to the San Jose Sharks on Wednesday.
It was the second of three meetings between the two teams this season. Nashville humbled the Oilers 6-0 in their only other game this season on March 8. ... Rinne came into the game having been yanked in both of his previous starts. Rinne was pulled in the second period of Thursday's 7-4 loss to Vancouver after allowing four goals on 12 shots faced. On Friday in Calgary he was lifted after giving up a goal on both shots he faced in the first eight minutes. ... Coming into the match, the Predators had gone to overtime or a shootout in 11 of their first 28 games, tied for the highest total in the NHL ... Nashville forwards Colin Wilson, Paul Gaustad and Patric Hornqvist were all out with upper-body injuries. Defenseman Hall Gill (lower body) was also absent. ... The Oilers were without forward Eric Belanger (groin), however fellow forward Ryan Jones and defenseman Mark Fistric returned to the lineup. ... Predators defenseman Scott Hannan left the game with an upper-body injury.