Callahan also scored in regulation and picked up an assist for the Rangers, who snapped a five-game losing streak. Lauri Korpikoski, Markus Naslund and Paul Mara each had a goal, while Scott Gomez recorded two helpers. Henrik Lundqvist made 26 saves to earn his 25th win of the season.
Mike Green lit the lamp twice for the Capitals, who have dropped two of three. Green has been deadly with the lumber of late, scoring in seven straight games to match an NHL record for the longest goal-scoring streak by a defenseman. Boston's Mike O'Connell set the record during the 1983-84 season.
A leading candidate for the Norris Trophy as the NHL's best defenseman, Green leads all rearguards with 21 goals and 49 points this year, despite missing 13 games due to injury.
Tomas Fleischmann and Eric Fehr both registered a goal and an assist, while Jose Theodore stopped 28 of the 32 shots he faced.
With the game deadlocked at 4-4 after 40 minutes of action, New York wasted several opportunities to break the tie. Washington was guilty of four consecutive infractions in the third period, including a double-minor on defenseman Shaone Morrisonn for high-sticking, but the Rangers' inept power play unit, which entered play ranked 27th in the league, failed to convert and the game was ultimately decided in a shootout.
After a scoreless first round in the extra segment, Nigel Dawes used a quick release to beat Theodore. Lundqvist then denied Sergei Fedorov and Nikolai Zherdev had a chance to cement the win, but Theodore made a save with the left pad, allowing Alex Ovechkin to extend the shootout to a fourth round. Callahan ripped a shot that caught iron and ricocheted off Theodore before dribbling across the goal line. Lundqvist then turned away Brooks Laich to seal Washington's fate.
New York got on the board first as Callahan streaked down the slot and shoveled a feed from Korpikoski past Theodore's blocker 7:33 into the contest.
Washington then countered with two tallies in the first period to seize the lead.
Fleischmann fanned on his initial bid from atop the right circle, but he continued to drive the net and roofed the disc past the catching glove of Lundqvist with 9:09 remaining.
Fehr was then the beneficiary of a fortuitous carom in the latter stages of the opening frame. Fleischmann was aggressive on the forecheck and emerged from the right corner with possession of the puck. As he made his way to the enemy cage, Fleischmann lost the handle and a Rangers player accidently kicked the disc to Fehr, and the former first-rounder banged it home at the right side of the net with 1:52 to play.
Korpikoski tied the game at the 8:49 mark of the middle stanza, then Green restored the lead for the visitors, firing a wrister over Lundqvist's glove with 9:28 remaining in the second period.
Naslund quickly responded for the Rangers, evening things 67 seconds later. Dawes slipped a backhand feed over to Naslund and the veteran Swede tucked it in before a rocket off the stick of Mara gave New York a one-goal advantage with four minutes left in the second.
However, Green solved Lundqvist again with 57.6 seconds remaining for a 4-4 tie.