The Russian sniper, who had already won the Art Ross Trophy as the leading scorer for the second time in four seasons, also collected the Ted Lindsay award, which goes to the league's most valuable player as voted by members of the NHL Players Association.
Lundqvist consoled himself with a Vezina Trophy win as top netminder, to deny Nashville Predators' Pekka Rinne and Los Angele Kings' Stanley Cup winner Jonathan Quick.
Stamkos also went home with some silverware accepting the Maurice Richard trophy as the NHL's leading goal scorer with 60.
Ottawa Senators' Erik Karlsson, who signed a seven-year $45.5 million deal on Tuesday, walked away with the Norris Trophy as the NHL's top defenseman edging Nashville Predators' Shea Weber and Boston Bruins' Zdeno Chara.
The 22-year-old blue-liner led all defensemen with 78 points (19 goals, 59 assists) 25 more than his nearest challengers.
Ken Hitchcock, who took over behind the bench of the St. Louis Blues early in the season, was the runaway winner of the Jack Adams award as coach of the year, easily out-pointing New York Rangers John Tortorella and the Senators' Paul MacLean.
Taking over for Davis Payne on November 6 after the Blues' sluggish start to the season, Hitchcock transformed his team into Stanley Cup contenders and set franchise records for wins(49) and points on the way to finishing second in the Western Conference.
The Blues' Doug Armstrong also picked up general manager of the year honours, partly for his bold move to hire Hitchcock.
Colorado Avalanche's Gabriel Landeskog, the second overall pick in last year's draft, beat out top pick Ryan Nugent-Hopkins of the Edmonton Oilers for the Calder Trophy and rookie of the year honours.
Other award winners included Boston Bruins' Patrice Bergeron, who picked up the Selke Trophy as top defensive forward while Florida Panthers' Brian Campbell became the first defenseman since 1954 to take home the Lady Byng as the league's most sportsmanlike player.