Antero Niittymaki stopped 47 shots for the 500th victory.
The Lightning have won two straight since losing five in a row - and 12 of 14 - to fall to the brink of elimination in the Eastern Conference playoff race.
Niittymaki stopped 19 shots in the third period as Boston tried furiously but belatedly to come back from a three-goal deficit.
Tuukka Rask made 13 saves for Boston, which has won just two of its last 14 home games.
Stamkos scored just 49 seconds into the game and then added another with 26 seconds remaining in the second period to make it 4-2 and give him 45 for the season. That equals Washington's Alexander Ovechkin and Pittsburgh's Sidney Crosby for the NHL lead.
Martin St. Louis also scored for Tampa Bay. Zdeno Chara, Johnny Boychuk and Mark Recchi scored for Boston. The Bruins are eighth in the Eastern Conference, two points head of Atlanta for the final playoff spot.
At San Jose, California, Evgeni Nabokov made 27 saves for his 50th career shutout as San Jose clinched a playoff berth while climbing back atop the Western Conference.
Defensemen Dan Boyle and Rob Blake scored power-play goals in the second period for San Jose, which has won two straight after a 0-5-1 skid over the previous 10 days.
Logan Couture also scored.
At Newark, New Jersey, Chris Drury scored the equalizer with 16.5 seconds left in regulation and Erik Christensen had the only tally in the shootout for New York.
Christensen scored on the first attempt of the shootout, and Henrik Lundqvist made it stand up with saves against Zach Parise, Patrik Elias and Travis Zajac. The Rangers, 10th in the Eastern Conference, moved within three points of eighth-place Boston and five behind No. 7 Philadelphia.
Jamie Langenbrunner and Elias both scored tiebreaking goals in the third for the Devils, who regained first place in the Atlantic Division over Pittsburgh.
At Atlanta, Mikhail Grabovski's tip-in 39 seconds into overtime gave Toronto the victory, damaging Atlanta's playoff hopes.
Toronto rookie Jonas Gustavsson stopped 19 shots for his sixth straight win. Atlanta's Zach Bogosian and Toronto's Phil Kessel traded goals in the first period.
The Thrashers closed within two points of eighth-place Boston for the final playoff spot in the Eastern Conference.
At Raleigh, Chad LaRose scored in the fifth round of a shootout to lift Carolina past Eastern Conference-leading Washington.
The contest marked the first time three rookie defensemen - Carolina's Jamie McBain and Bryan Rodney and Washington's John Carlson - have scored goals in a game since Toronto and Chicago did it on March 8, 1947.
Alexander Semin also scored for the Capitals.
At Columbus, Antoine Vermette had two goals and an assist, and Columbus scored four second-period goals to hand Chicago its worst loss of the season.
The Blackhawks missed a chance to clinch a playoff berth on their own, but secured a spot when Calgary lost to the New York Islanders.
Kristian Huselius also scored twice, and Mike Commodore, Andrew Murray, Jackub Voracek - on a penalty shot - and rookie Mike Blunden also found the net. Kris Versteeg, Tomas Kopecky and Adam Burish scored for Chicago.
At Philadelphia, Kyle Brodziak scored in overtime for Minnesota, sending the Flyers to their sixth loss in seven games.
Martin Havlat, Andrew Brunette and Marek Zidlicky also scored for the Wild.
Oskars Bartulis, Simon Gagne and Dan Carcillo scored for the Flyers. Philadelphia is seventh in the Eastern Conference, four points ahead of ninth-place Atlanta in the race for the eight playoff spots.
At Uniondale, Matt Moulson and Bruno Gervais scored third-period goals in the New York Islanders' comeback victory.
Trent Hunter had his first goal since Jan. 19 to help the Islanders end a three-game losing streak. Eric Nystrom had a goal and an assist for his first multipoint game in almost six months, and Nigel Dawes also scored for the Flames. Calgary is four points behind idle Detroit for the final playoff spot in the Western Conference.
At Nashville, David Legwand scored the shootout winner for the home team after Steve Sullivan, Patric Hornqvist and Dan Hamhuis connected in regulation.
Lee Stempniak, Wojtek Wolski and Keith Yandle scored for Phoenix.
Nashville has won seven of its last eight. After winning nine consecutive games, the Coyotes have lost their last two.
At Montreal, Brian Gionta scored twice - including Montreal's second empty-net goal - and Jaroslav Halak made 23 saves.
Tomas Plekanec and Benoit Pouliot scored for the Canadiens. Halak lost his bid for a shutout when Radek Dvorak scored with 3:36 left to draw Florida to 2-1.
At St. Louis, T.J. Oshie scored his first goal in 10 games, B.J. Crombeen and Paul Kariya also scored, and Chris Mason stopped 30 shots for St. Louis.
Dustin Brown scored for Los Angeles.
