His errant backhand during the morning skate caught teammate Martin St. Louis near the left eye, ending the Tampa Bay All-Star forward's consecutive games streak at 499.
Moore made up for it later when he scored a dramatic short-handed goal to tie the game against the New York Rangers with 1:57 left and then netted the only goal of the shootout in the Lightning's 3-2 win on Thursday night.
It took all of that for the Lightning to snap a five-game losing streak and keep the Rangers from their 2,500th win in franchise history.
"We really wanted to win this one for Marty," said the 31-year-old Moore, who broke into the NHL with the Rangers. "We just wanted to hang in there. Sometimes something really good can come out of adversity. It certainly feels great to get this win."
Moore's short-handed goal came on a slick backhand as he sped by two defenders before beating goalie Henrik Lundqvist to the glove side. He also fooled Lundqvist to the same spot with a forehand wrist shot in the shootout.
"I don't score too many goals so they were satisfying," said Moore, who has 65 career goals. "Hopefully we can build from this game."
The Lightning were able to end their skid despite not having St. Louis in the lineup. He sustained facial and sinus fractures when the shot by Moore at the morning skate hit him in the face.
"Losing a leader is never easy, but we found a way tonight," Lightning coach Guy Boucher said.
Ryan Malone had gotten Tampa Bay even at 1 in the second period.
Callahan and Artem Anisimov scored for the Rangers, who have dropped two straight (0-1-1) following a five-game winning streak.
The Rangers were again denied from becoming the fifth NHL team to record 2,500 wins. The Chicago Blackhawks are the only other Original Six team not to reach the mark.
New York (15-6-4) lost for only the fourth time in 16 games. The Lightning improved to 12-14-2.
"We knew they would be desperate," said Lundqvist, who has started all 26 games for the Rangers against the Lightning since 2005. "We had a couple of big chances to kill the game. Instead they came back and tied it. We just have to move on."
Anisimov's goal at 13:23 of the second led to a fracas after Lightning captain Vinny Lecavalier vigorously objected to Anisimov's spirited celebration. After scoring, Anisimov dropped to one knee and held his stick by the blade and pointed the straight end at Garon.
"It was disrespectful to point directly at our net and our goalie," Lecavalier said.
The subsequent fight resulted in a combined 38 penalty minutes among two Rangers and three Lightning players. Anisimov received the most with a four-minute penalty for roughing, an extra penalty for unsportsmanlike conduct, and a 10-minute misconduct. Tampa Bay's Steve Downie, who left the bench to join the brawl, was assessed a roughing penalty and a misconduct.
"He was wrong and he knows it," Rangers coach John Tortorella said of Anisimov, who wasn't made available by the Rangers after the game. "He apologized to his teammates and we will move on from this."
Callahan's power-play goal at 7:49 of the first gave the Rangers a 1-0 lead. However, New York dropped to 12-1-1 in games in which it scored first. Malone's sixth of the season tied it at 11:23 of the second. Malone intercepted a pass by Ryan McDonagh in the defensive zone before beating Lundqvist for the unassisted goal.
The 36-year-old St. Louis hadn't missed a game since Nov. 15, 2005, at Washington. He was scheduled to return to Florida on Friday, and will be evaluated by team doctors after the swelling near his eye subsides, the team said. He was spending Thursday night in at a New York hospital, according to the Lightning.
The Rangers were without defenseman Michael Sauer, who sustained a concussion when he collided with Toronto defenseman Dion Phaneuf on Tuesday. New York has been without defenseman Marc Staal all season because of concussion symptoms.
The Rangers' first win was on Nov. 16, 1926, a 1-0 home victory over the Montreal Maroons on a goal by captain Bill Cook. ... Tampa Bay was also missing injured defensemen Pavel Kubina and Mattias Ohlund. . Calgary D Jay Bouwmeester has the league's longest current consecutive-game streak at 532. St. Louis' was the third longest. . The Rangers' six regulation losses are the fewest in the NHL. ... New York's Richards -- who assisted on Callahan's goal -- has a seven-game point streak. He has nine goals and 10 assists in the last 17 games.