Stamkos had three goals to become the first player from the 2008 draft to reach 700 points, and the NHL-leading Lightning won their seventh consecutive game by beating the New York Rangers 6-3 on Monday night.
''Stammer is finding his groove,'' Tampa Bay coach Jon Cooper said.
Stamkos scored power-play goals that tied the game in the first and second periods. The center completed his ninth hat trick and first since Oct. 13, 2014, against Montreal from the slot at 10:41 of the third.
''I knew it had been a while,'' Stamkos said with a laugh. ''I don't know the exact date . I don't want to hear it.''
The Lightning star, coming off a two-goal, two-assist outing in Saturday night's 7-1 win over the Colorado Avalanche, has 701 points in 696 career games. He joins Martin St. Louis (953) and Vincent Lecavalier (874) as the only Tampa Bay players reaching the 700-point milestone.
''To be able to beat some of the best teams, you have play really strict and smart, and make the right decision with or without the puck,'' Lundqvist said. ''So, the next time we play a top team like this we need to do all those things.''
New York defenseman Kevin Shattenkirk left in the second period with an upper-body injury. He took a check around the left shoulder and had a sling on his left arm postgame.
Rangers coach David Quinn had no update after the game on Shattenkirk, who will be evaluated Tuesday.
Stamkos scored from the left circle while falling down at 6:19 of the second before McDonagh put Tampa Bay up 3-2 with 7:18 left in the period.
''Nothing kind of seems to phase us,'' McDonagh said.
Cirelli extended his goal streak to three games 24 seconds before Stamkos' third goal of the goal.
Fast and Cirelli, with an empty-netter, had late third-period goals.
The Rangers took a 1-0 lead 12:19 into the game when Hayes had a backhander from the left circle deflect off McDonagh's skate.
After Stamkos scored at 14:09 of the first, Hayes made it 2-1 with a rebound goal just 58 seconds later.
The Lightning went 2 for 6 with the man advantage.
''Take that many penalties, you're not going to beat Tampa,'' Lundqvist said. ''That's just the way it is. We can work really hard and do a lot of good things but it's too important in the game. Hopefully we really learned a lesson.''
New York failed to score on its lone power-play.
''Ten minutes extra killing penalties is just not a recipe to have success in this league or any league really,'' Quinn said.
NOTES: New York has been ahead after the first just seven times (3-3-1). . Lightning RW Nikita Kucherov had an assist and has 22 assists and 27 points over his last 14 games. . Rangers RW Mats Zuccarello (groin) sat out his seventh consecutive game but is nearing a return. ... Tampa Bay is 9-0-0 against the Metropolitan Division.
Rangers: Return home Friday night against Vegas.
Lightning: Host Toronto Thursday night.
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