Forsberg's goal was his team-leading 10th of the season. Nashville goaltender Pekka Rinne stopped all 37 shots he faced, including a penalty shot in overtime, to earn his second shutout of the season.
"These are huge points for us," Rinne said. "You keep playing every second night, and that's some huge points we've been gathering up here at home."
Forsberg had some bad luck the past two games with hitting posts. He had hit one in each game, including one earlier in overtime against Edmonton. It was a relief for him to get the game-winning goal.
"It was huge for the team that we could get the two points in a game that we didn't play our best game for two periods," Forsberg said. "I think we kind of stepped up there in the third and took it to them a bit more. It was a big win, for sure."
The goal came at the end of a shift where Forsberg had been on the ice for 1:17. He was able to spin his way around Edmonton forward Taylor Hall and put the shot on net. Hall had been on the ice for 1:23.
"I was really tired, so I was just trying to get it on net," Forsberg said. "I don't know if it was a screen or something. I was just really happy that it went in."
The Predators are now 9-1-1 at Bridgestone Arena, and alone in first place in the Central Division two points clear of the St. Louis Blues. The Oilers have now lost eight straight games (0-6-2) and remain winless in 13 tries (0-11-2) against the Western Conference.
"It's hard to take when our guys play that hard," Oilers coach Dallas Eakins said. "To a man, our guys worked extremely hard against a team that may be the hardest-working team we've seen this year. I thought we matched their work ethic, and that's a tough one to take."
Edmonton came out strong in the first period and controlled the majority of the play throughout the first half of the period. Rinne made some big saves to keep Edmonton off the scoreboard early.
"It seems like every time you come in here, they come out stomping," Eakins said. "The old saying in hockey is 'weather the storm.' I put the notion in their heads that we don't want to weather the storm, we want to push just as hard and matched their work ethic. I thought our guys exceeded that in the first period.
Nashville had two power-play chances in the second period but was unable to generate much zone time, even with the man advantage. Edmonton's penalty-killing unit did a good job of preventing the Predators from entering the offensive zone.
Defenseman Seth Jones appeared to give the Predators a 1-0 lead late in the second period, but the goal was immediately waved off by the officials. Paul Gaustad was ruled to have made incidental contact with Edmonton goaltender Viktor Fasth, who finished the game with 24 saves.
The Oilers had several high-quality opportunities in the second period and then the teams traded chances in the third. Rinne and Fasth each made key saves from point-blank range.
Edmonton forward Jordan Eberle had a chance to win the game 13 seconds into overtime on a penalty shot. Rinne was able to stay patient and make a sprawling left pad save.
"He's really nifty in penalty shots," Rinne said. "I think he's one of the better shooters stats wise in the NHL in penalty shots and shootouts. You just try to stay patient with a guy like that. He has multiple different moves, and this time I thought he got a little bit too close to me and I was able to put my leg over there and he couldn't put it over my leg. Obviously at the time in OT, that's a big save and I'm happy I made that save."
Nashville went 0-for-5 on the power play for the night, making it the ninth consecutive home game that it hasn't scored a power play goal at home. Nashville has gone 1-for-37 on the power play at home this season.