Nikita Kucherov had two assists, and Andrei Vasilevskiy made 23 saves for the Lightning (33-20-4), who have allowed a total of 12 goals during the winning streak.
"We have not given up much the last few games," Vasilevskiy said. "Playing good defense and when we have scoring chances we're scoring goals. It's simple."
Leon Draisaitl scored for the sixth straight game and extended his point streak to nine games for the Oilers (34-20-4), who have lost four in a row. Stuart Skinner made 32 saves.
Edmonton has been outscored 17-7 in losing its first three games since the break for the 4 Nations Face-Off.
"We're a fragile group right now and we're reluctant to play our game," Oilers coach Kris Knoblauch said. "Confidence is a little hard right now. I think everyone's a little discouraged. They put a lot of pressure on themselves to win and they view themselves as one of the best in the League. We've got to put those adversity moments behind us."
Draisaitl gave Edmonton a 1-0 lead with a power-play goal at 11:53 of the first period. Draisaitl and Connor McDavid executed a give-and-go, with Draisaitl sending a snap shot past Vasilevskiy from low in the right face-off circle.
"We're in a bit of a hole right now as a team," Oilers defenseman Mattias Ekholm said. “It's about resiliency, it's about sticking with it. We're going to have to dig one out sooner or later."
Draisaitl leads the NHL with 43 goals and has scored seven during his goal streak. He has 13 points (eight goals, five assists) during his point streak and has had at least one point in 17 of his past 18 games (28 points; 14 goals, 14 assists).
Michael Eyssimont tied it 1-1 at 13:11 after he forced a turnover in the neutral zone and went to the backhand to beat Skinner from the low slot off a pass by Gage Goncalves.
"There are a lot of momentum swings in a game, especially when there are a lot of great players on each team," Eyssimont said. "So just to take it right back was important."
Brandon Hagel put Tampa Bay ahead 2-1 lead 29 seconds into the second period when he scored on a wraparound, beating Skinner to the left post.