Chimera one-timed a pass through the crease from Marcus Johansson past Henrik Lundqvist to break a scoreless tie 2:11 into the second period.
The Caps doubled their lead at 4:08 on a power play when Lundqvist gave up a long rebound on a Mike Green slap shot and Arnott was there to fire it home.
Michal Neuvirth recorded a 22-save shutout for the top-seeded Capitals, who will take a commanding advantage into New York for Sunday's Game 3.
Lundqvist finished with 16 saves for the eighth-seeded Rangers.
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