Stamkos, who also had an assist, tied the record (383) with a power-play goal at 12:57 of the second period to cut Detroit's lead to 3-1.
"When you are a kid, you dream about playing in the NHL, but you don't dream of becoming a team's franchise leader in scoring," Stamkos said. "Hopefully, I'll score a lot more, but right now, it is an honor to share the record with a world-class guy like [Lecavalier]."
[WATCH: All Lightning vs. Red Wings highlights]
Nikita Kucherov had two goals and two assists to give him 115 points (35 goals, 80 assists), the most in the NHL since Pittsburgh Penguins center Sidney Crosby had 120 points (36 goals, 84 assists) in 2006-07.
"We're never surprised by anything he does," Stamkos said. "That's probably the greatest compliment you can get in this League, you are expected to go out and do special things game after game."
Video: TBL@DET: Kucherov blasts PPG to even the score
Brayden Point had a goal and two assists, and Andrei Vasilevskiy made 23 saves for Tampa Bay (54-13-4), which tied its record for wins and road wins (25) in a season (previously set in 2017-18). The Lightning lead the Boston Bruins by 19 points for first place in the Atlantic Division and the San Jose Sharks by 18 points for the Presidents' Trophy.
"Our start wasn't what we wanted," Lightning coach Jon Cooper said. "We've had a few days off since a good win over Toronto (6-2 on Monday), and there are times that's just as hard as a day off. Detroit did what they needed to do and made it tough for us, but we felt we could still get back into the game."
Video: TBL@DET: Point buries own rebound from the slot
Jimmy Howard made 34 saves for Detroit (24-37-10), which has lost four in a row and 12 of its past 13 (1-9-3). The Red Wings, who have been eliminated from Stanley Cup Playoff contention, have lost 15 straight games to Tampa Bay (0-13-2), the longest streak against one team in their history.
"That's just a great hockey team," Red Wings coach Jeff Blashill said. "My belief has always been that you need three elite players to be a contender in this League. Tampa Bay probably has five or six."
Madison Bowey gave the Red Wings a 1-0 lead at 2:20 of the first period, and Darren Helm made it 2-0 at 10:24 after forcing a turnover while shorthanded and scoring five-hole on a 2-on-1 for his 100th NHL goal.
"It was great to get 100 goals, because this is a tough League and it means I've been here for a while," Helm said. "It is extra special to get it shorthanded, though, because I've spent a lot of time killing penalties."
Video: TBL@DET: Helm nets SHG for 100th career goal
Justin Abdelkader extended the lead to 3-0 at 3:43 of the second period. It was his first goal since Dec. 8 (41 games).
Cooper then decided to play Kucherov, Point and Stamkos together 5-on-5 instead of only using them together on power plays.
"We knew with this group of guys that we could still get back into the game if we started playing the right way," Cooper said. "We needed a spark, and they obviously had a huge third period. That line is a great ace to have in the hole."
Point made it 3-2 at 1:46 of the third period on his own rebound in the slot, and Kucherov tied it 3-3 at 8:24 with a one-timer from the right circle on the power play.
Tyler Johnson scored 26 seconds later on a redirection to give the Lightning a 4-3 lead.
Kucherov made it 5-3 at 16:38, but Michael Rasmussen cut it to 5-4 at 18:18 with Howard pulled for the extra skater.
Video: TBL@DET: Kucherov pots second goal on pretty move
They said it
"[Lecavalier] is an icon in this franchise, which is why his number is in the rafters in our rink, but we've got two unreal players who have had great years. Kucherov broke [Lecavalier's] season record for points, and now Stamkos has tied him for goals. That shows you how valuable they are to this team." -- Lightning coach Jon Cooper
Video: Dunkin' NHL Comebacks: Lightning topple Red WIngs
"I think there are a lot of ways they compare to the old Red Wings, just as far as they are built. They can beat you so many ways - on the forecheck, on the power play, even their [penalty kill] is the best in the League - and then they've got a world-class goaltender." -- Red Wings defenseman Niklas Kronwall
Need to know
Kucherov is the first NHL player to have at least 80 assists in a season since Henrik Sedin had 83 for the Vancouver Canucks in 2009-10. … Red Wings forward Dylan Larkin (neck) could return as soon as Saturday. … Tampa Bay is the fourth team in NHL history to record at least 54 wins in consecutive seasons, joining the Washington Capitals (56, 2015-16; 55, 2016-17), Bruins (57, 1970-71; 54, 1971-72) and Montreal Canadiens (58, 1975-76; 60, 1976-77; 59, 1977-78).
Lightning: Host the Washington Capitals on Saturday (7 p.m. ET; NHLN, SUN, NBCSWA, NHL.TV)
Red Wings: Host the New York Islanders on Saturday (1 p.m. ET; FS-D, MSG+, NHL.TV)
Video: Lightning score five straight goals in 5-4 win