TAMPA -- The Tampa Bay Lightning extended their season-high winning streak to six straight games on Tuesday night, getting a short-handed goal from center Brian Boyle in the third period to beat the Edmonton Oilers 6-4 at Amalie Arena.

The Lightning (25-17-4) saw a two-goal lead disappear in the third period, only to get it back on Boyle's goal with 12:18 remaining, answering a short-handed goal earlier by the Oilers (19-24-5). Defenseman Braydon Coburn flipped a high dump pass into the Oilers zone, and Boyle got to the puck before the advancing Oilers goalie, Anders Nilsson, cutting wide and firing the puck into the empty net for his ninth goal of the season. The goal was just the third short-handed goal for the Lightning this season, and the third allowed by the Oilers.

"It kind of stopped right where it landed. That's a great bounce for us," Boyle said. "The goalie wanted to come out and play it, and I put him in a tough spot."

Tampa Bay added an empty-net goal from center Alex Killorn (his eighth) with 26.7 seconds left after Edmonton had pulled Nilsson for an extra attacker. The six goals match a season high for Tampa Bay.

"It seems like everybody is contributing the way they should. It's nice that we're finally scoring some goals," Lightning coach Jon Cooper said. "When you get the lead, you're forcing them to keep chasing you. They get that fourth goal, you could get on your heels a little bit. They get a power play and we get a shorty to win."

Down 4-2 to open the third period, the Oilers rallied to tie the game with two goals in a span of 2:19. The first came on a 2-on-1, with left winger Taylor Hall feeding center Leon Draisaitl for his 11th goal of the season, pulling within 4-3 with 17:50 left in the game. Then with 15:31, right winger Iiro Pakarinen fired a wide shot that went between two Lightning players and beat goalie Andrei Vasilevskiy to tie the game at 4-4, his fourth goal of the season.

With two backup goalies squaring off, the two teams alternated on five goals early, with the Lightning taking early leads three times, the first two quickly answered by the Oilers before the Lightning pulled away to a 4-2 lead late in the second period.

Lightning defenseman Nikita Nesterov opened the scoring, getting his third goal just four minutes into the game, beating Nilsson off a cross pass from Killorn.

Just 88 seconds later, Oilers right winger Zack Kassian got his first goal of the season, scoring on a rebound off a shot from Pakarinen.

The Lightning jumped back ahead 2-1 on right winger Nikita Kucherov's goal with 3:03 left in the first -- his third in two games and his 19th of the season.

Again, Edmonton answered, with a short-handed goal with 33 seconds left in the first by center Mark Letestu, his seventh of the season. Letestu's goal was just the second short-handed goal by the Oilers this season, and just the third allowed by the Lightning this season, beating Vasilevskiy.

"We didn't seem to have the best legs tonight," left wing Matt Hendricks said of the team playing a back-to-back after beating Florida on Monday night. "I don't think we had quite the jump our club usually has. Nilly made some big saves for us early and kept us in it, and Pakarinen was a wrecking ball out there tonight. He was a freight train."

That tied the game at 2-2, until Palat scored his eighth goal of the season with 13:51 left in the second period. Palat pushed the puck up the left side, and center Vladislav Namestnikov made a pass back to him as he fell to set up the go-ahead goal and a 3-2 lead.

Palat set up the fourth goal as well -- his shot caromed off the pad of Nilsson and went straight up, coming down behind the goalie, and Namestnikov saw the puck in the air and knocked it in from behind the goal for a 4-2 lead with 2:48 left in the second. The goal was reviewed to see whether Namestnikov touched the puck above the top of the goal, but the goal was upheld for his 10th goal of the season.

"We beat ourselves tonight," Letetsu said. "Tonight we gave easy offense. Breakdowns, just not competing in areas, having lapses out there. We beat ourselves, plain and simple, tonight."

NOTES: The Lightning, finally back to full strength after a long rash of injuries, had D Matthew Carle and C Jonathan Marchessault as healthy scratches. ... The Oilers, already short-handed with injuries, lost RW Nail Yakupov to a right leg injury just five minutes into the game. Yakupov was tangled up with Lightning D Braydon Coburn and both went down, with the Russian being helped off the ice. Yakupov, who just returned last week after missing 22 games with an ankle injury returned later in the period. ... Edmonton had C Rob Klinkhammer, who was just recalled Tuesday from the AHL, LW Luke Gazdic and LW Lauri Korpikoski as healthy scratches.