Holtby, who has become a playoff hero after playing in just seven games during the regular season, made 30 saves.
With the Eastern Conference semis tied at 3-3, New York will host Game 7 Saturday. The winner of that one will take on the New Jersey Devils, with a berth in the Stanley Cup Finals on the line.
Both New York and Washington survived a Game 7 in the opening round of the playoffs. The Rangers downed Ottawa 2-1 in their deciding contest and Washington defeated Boston 2-1 in overtime in the concluding game of their series.
This will be the only one of the second-round series to go a full seven games after three of the eight opening-round matchups went the distance.
New York's Anton Stralman was sent off for tripping just 1:13 into the game and it took Alex Ovechkin only 15 seconds of power-play time to produce the opening goal.
Jason Chimera tipped in a shot midway through the second period to expand Washington's lead.
New York's only goal came with 51 seconds remaining in the third period when Marian Gaborik beat Holtby with a slap shot.
Holtby was forced into action late in the season and then in the playoffs when both Tomas Vokoun and Michal Neuvirth suffered injuries.