Also nominated for the award were Ben Bishop of the Tampa Bay Lightning and Tuukka Rask of the Boston Bruins. The winner will be honoured June 24 at the league's awards banquet.
Varlamov broke Colorado head coach Patrick Roy's club record for most wins in a season. He ranked first in the NHL in shots faced (2,013) and saves (1,867) but thrived under the heavy workload, posting a 7-1-1 record when facing 40 or more shots and going 32-4-4 when facing 30-plus shots.
Bishop won a club-record 37 games for Tampa Bay and also set a franchise mark with a .924 save percentage. He finished tied for fourth overall in shutouts (five) and seventh with a 2.23 goals-against average in being named a Vezina Trophy finalist for the first time.
Rask recorded a 36-15-6 record in helping Boston capture its first Presidents' Trophy since 1990. He finished first overall in shutouts (seven), second in save percentage (.930), fourth in goals-against average (2.04) and fifth in wins.