With the score tied 1-1, Callahan carried the puck into the right circle and intended to send a pass across the crease to Ruslan Fedotenko.
Fedotenko also scored on a first-period power play.
Martin Biron turned aside 27-of-28 shots for the Rangers, who wrapped up a season-opening, seven-game road trip with a 3-2-2 record.
Nik Antropov scored and Mason stopped 15 shot for Winnipeg.
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