Jordan Eberle scored two goals, and the Oilers snapped a four-game losing streak with a 5-3 victory Sunday night.
After taking a 3-1 lead in the first period, the Oilers fell apart in the second and allowed the Lightning to tie it.
"We were turning pucks over in our own end. It was the same old story with this team," Eberle said. "But as soon as they tied it, we found a way to get back to playing the way that got us the lead in the first place. That's what won us the game."
Taylor Hall, Luke Gazdic, and Boyd Gordon also scored for the Oilers (14-26-5), who have won three of 13. Edmonton, which has the NHL's second-worst record, avoided its fourth five-game losing streak of the season.
"There were certainly some shifts in the second period where we didn't play well, but for the most part our effort was good," Hall said. "Our execution was good. There have been a lot of times this season where we have gone into a third period tied or in a close game and we just haven't really played the way we should. Tonight was a different story.
"It was nice to see, especially against a team that is as good and as high in the standings as Tampa."
It was the Oilers' first win against a team above the playoff cutline in a month.
"We need to spin this into a positive," Gordon said. "Hopefully we can get things turned around here and start playing some winning hockey."
"I thought we owned that second period and we had a bad break for us on the fourth goal and then a good play by them on the fifth one," Hedman said. "That's not the way we wanted to come out of this.
"We were carrying the momentum going into the third. It's obviously frustrating that we didn't play better in the third."
Tampa Bay took a 1-0 lead with a power-play goal 2:43 into the game. Matthew Carle made a cross-ice pass to Kucherov at the left faceoff dot, and Kucherov beat goalie Ilya Bryzgalov with a quick shot glove-side.
Edmonton tied it 1:35 later when a stick got caught in the skates of Lightning forward Martin St. Louis in front of the Tampa Bay net. Eberle fished it out and lifted his 13th goal of the season past goalie Ben Bishop.
"I have no idea," coach Jon Cooper said when questioned about Bishop's status. "I don't ask, so I can look you in the eye and say I don't know.
"It's hard to speculate. I don't know what the injury is, but I don't think it's going to be major serious. I hope not anyway. But if it is, then [Anders Lindback] is a proven goaltender in the league."
Edmonton went ahead 2-1 during the first half of the power play on their second shot of the game at 6:09. Eberle's shot pinballed in front and was deflected past Lindback by defender Sami Salo. It was Eberle's second goal in less than two minutes after he netted only one in his previous 11 games.
The Oilers took a two-goal lead with 4:18 left in the first. A Lightning giveaway behind their net eventually allowed Gazdic to tip his second career goal past Lindback off a point shot from Justin Schultz.
The Lightning gained momentum in the second when Hedman scored his eighth of the season at 8:47. Hedman scored with a screened shot after Tampa Bay stole the puck at the Oilers' blue line.
Tampa Bay tied it 3-3 with 5:35 remaining in the second when Filppula scored his 16th goal with a quick wrist shot.
Lindback kept the Oilers from regaining any momentum on a late second period power play, making stops on Eberle and Gordon.
Both teams hit posts early in the third, including one by Edmonton's Ales Hemsky that prompted the goal judge to turn on the red light before a video review determined the puck didn't go in.
Edmonton took a 4-3 lead at 8:20 when Gordon fought off a defender and swatted in the rebound from his own backhand for his second goal in two games.
The Oilers went up by two goals with 9:30 remaining when the teams were playing 4 on 4. Hall made a perfect redirection of Andrew Ference's point shot for his 16th goal and team-leading 41st point.
The teams split the two-game season series. ... Tampa Bay forward Steven Stamkos (broken right tibia) has begun skating in full gear but isn't ready to play. The Lightning are 13-8-4 without the star center. ... Bishop was 8-0-2 in his previous 10 games, allowing two goals or fewer in eight consecutive starts and in 26 of 31. ... Lightning D Sami Salo returned to the lineup after sitting out four games due to an upper-body injury. ... Eberle was back after a one-game absence because of a knee injury.