Crosby on Tuesday also won the Ted Lindsay Award as the league's outstanding player as voted by his peers.
The 26-year-old Canadian superstar won his second Hart Trophy after leading the NHL with 104 points this season, registering at least one point in 60 of the 80 games he played.
He scored 36 goals and led the league with 68 assists to capture his second Art Ross Trophy as the NHL's top scorer.
Crosby, who also won the Hart Trophy in 2007 and finished runner-up in the voting in 2010 and last season, was a near- unanimous choice to win after garnering 128 first-place votes of 137 ballots cast.
Getzlaf scored a career-high 31 goals and finished second in the NHL with 87 points to help Anaheim to the top record in the Western Conference.
He had a 14-game point streak from November 15-December 15, the longest in the NHL since the 2011-12 season.
The 28-year-old Canadian, a first-time Hart finalist, failed in his bid to join teammate Corey Perry (2011) as the only Anaheim player to win the award.
Giroux was also a Hart finalist for the first time after finishing third in the scoring race with 86 points. He matched a career best with 28 goals and had a great finish to the season with 79 points in his last 67 games to help the Flyers earn a playoff spot after a disastrous 3-9-0 start.
Finland's Rask helped the Bruins to a record of 36-15-6 and was the only goaltender to rank among the top five in all major statistical categories.
He led the league with seven shutouts, was second in save percentage at .930, finished fourth with a 2.04 goals-against average and was fifth in wins. Rask allowed two goals or fewer in 37 of his 58 starts.
- Roy adds to legacy -
Patrick Roy, a Hall-of-Fame goaltender who guided the Colorado Avalanche to a 52-22-8 record in his first season as a head coach, won the Jack Adams award as the league's top coach.
The 48-year-old Quebec City native oversaw a historic turnaround as the Avalanche followed up their 29th-placed finish in the overall standings in 2013 with a third-place finish this year.
Roy benefitted from having at his disposal dynamic forward Nathan MacKinnon, who won the Calder Trophy as top rookie of the season.
MacKinnon, at 18 the youngest player to earn the award, led all first-year players with 63 points and 39 assists, while tying for the top spot with 24 goals.
His 13-game point streak topped legendary Wayne Gretzky's mark of 12 consecutive games with a point by a player aged 18-or-younger.
For the second time in the last three seasons, Boston Bruins forward Patrice Bergeron received the Selke trophy as the league's best defensive forward.