Lundqvist, who pulled the Rangers back from the brink of elimination with a 1-0 victory Sunday, came back with another stellar performance Monday, turning aside all 35 Capitals shots he faced.
The Swedish goalie's performance helped boost sixth-seeded New York into Round 2, where they will face the Boston Bruins, winners of their own Game 7 Monday against the Toronto Maple Leafs.
The Rangers beat Washington in a seven-game series for a second straight year.
Braden Holtby turned aside 22 shots for the third-seeded Capitals.
Jordana Brewster on Paul Walker: 'He was an enormous presence in my life'
Couple mistakenly served bag of cash at McDonald's drive-thru