DETROIT -- Before Friday's game, Tampa Bay Lightning general manager Steve Yzerman was asked if he planned to take away any mementos from his last game at Joe Louis Arena.

"Two points would be nice," said Yzerman, who captained the Detroit Red Wings from 1986 to 2006.

Consider it done, though it wasn't easy.

Nikita Kucherov scored at 3:28 of overtime to give the Lightning a come-from-behind 2-1 overtime win over the Detroit Red Wings on Friday.

Kucherov tipped home a Brayden Point pass from the edge of the goal crease for the winner.

The Lightning moved to within one point of the Boston Bruins and New York Islanders for the final wild-card playoff position in the Eastern Conference.

"Every game is huge for us right now," Kucherov said. "Every time you get a W, you are excited. We're just going to take one game at a time and see what's going to happen."

He was delighted to make a memory from his farewell appearance at the rink the Red Wings have called home since 1979. Detroit will move into Little Caesars Arena next season.

"The Russian Five played here, so for me it's special," Kucherov said.

For the past month, Kucherov has been special. Since Feb. 21, he leads the NHL in scoring with 17-12-29 totals.

"When Kuch is getting in that three-to-six-shot range, pucks go in for guys like him," Lightning coach Jon Cooper said. "That's what he's doing. He's creating space for himself, he's fighting through stuff.

"Your best players have got to be your best players and he's a big reason why we're back in this race."

After a three-game losing streak, the Lightning have now won two in a row in back-to-back nights over Boston and Detroit, and both on the road. Aware that the Bruins and Islanders face each other on Saturday, Cooper pulled no punches in assessing where they'd be without these consecutive triumphs.

"It would have been devastating for us, and that's the way it is when you're not trying to just catch one team but catch multiple teams," Cooper said. "It's hard to do.

"That's why you've got to sit there and say the only destiny you can control is your own."

For a long time Friday, it appeared as if that destiny would prove to be out of their control.

Red Wings captain Henrik Zetterberg opened the scoring at 8:03 of the second period. Zetterberg accepted a backhand pass from Gus Nyquist, and his fluttering wrist shot sailed over the shoulder of Lightning goalie Andrei Vasilevskiy, who appeared to be screened by teammate Brayden Point on the play.

Zetterberg has six points in Detroit's last five games. It was his 325th goal as a Wing, moving Zetterberg past Norm Ullman into sixth on Detroit's all-time goal scoring list.

The Lightning tied it 5:53 into the third period. Detroit goalie Petr Mrazek blocked Kucherov's point shot but Ondrej Palat escaped his checker, Riley Sheahan, and slammed the rebound into the net.

"The first two periods we didn't play well," Palat said. "The energy wasn't there, the execution wasn't there.

"We were just talking about we have to shoot more, we have to go in front of the net more. That's what happened."

With the assist, Kucherov extended his point streak to four games. He has nine points over that span.

Detroit's power play finished the night 0 of 5 and Wings coach Jeff Blashill viewed that as the difference in the outcome.

"We had five chances, a chance to win the game," Blashill said. "The one power play, the second one, we didn't get in the zone, so that was no good at all. I thought overall it had some moments but not good enough.

"We've got to make sure we're doing a better job on our entries. We need more speed on our entries."

NOTES: Henrik Zetterberg is Detroit's nominee for the Bill Masterton Memorial Trophy. Zetterberg, who underwent back surgery in 2013, leads the Wings in scoring with 61 points. ... Detroit F Darren Helm missed his third straight game due to a lower body injury. D Ryan Sproul (knee) was also a Wings scratch. ... Ds Jason Garrison (lower body) and Slater Koekkoek and Fs Tyler Johnson (lower body) and Cedric Paquette (lower body) were scratched for the Lightning. ... Lightning D Victor Hedman leads all NHL rearguards in power-play points with 4-25-29 totals. ... Tampa Bay has won four straight on the road but has lost three in a row at home and will play its next four games on home ice.