Selected in the first round (No. 9) of the 2008 NHL Draft, Bailey is the third to play 1,000 games with New York, joining Hall of Famers Denis Potvin (1,060) and Bryan Trottier (1,123).
"There was countless texts from friends and former teammates, family and everyone," the 33-year-old forward said. "Just overwhelming with the support and all the kind words."
Bailey, who has 557 points (178 points, 379 assists) in his NHL career, scored his 23rd career game-winning goal.
"For Josh, it's fun to see that," New York forward Brock Nelson said. "You can't write it any better, him getting the game-winner. Huge part of the franchise and this team, so well deserved."