The Lightning played without Martin St. Louis for the first time since the 2005-06 season. The veteran winger had been scheduled to play in his 500th consecutive game Thursday, but he was hit above the left eye by a puck during the morning skate at Madison Square Garden.
He had to be helped off the ice with blood flowing from the cut. St. Louis has nine goals and 13 assists in 27 games this season and has produced more than 90 points in each of the last two seasons.
Despite St. Louis' absence, the Lightning snapped a five-game losing streak.
In addition to delivering the only shootout goal, Moore tied the game by scoring shorthanded with 1:57 left in regulation.
Henrik Lundqvist stopped 29 shots for the Rangers, who have lost two straight.