Gagne, a playoff hero last season in the Flyers' run to the Stanley Cup finals, spent the first 10 seasons of his career with Philadelphia before being dealt to Tampa Bay during the summer to clear salary cap space.
Nikolay Zherdev and Danny Briere scored for Philadelphia.
Fans cheered within the first minute of the game, when Gagne stepped on the ice for his first shift of the night. The popular left winger received a louder ovation with 13:40 left in the first, when the Flyers showed a video montage of highlights during a timeout. Gagne waved to the crowd from the bench, then joined his new teammates for the resumption of play.
Stamkos beat Flyers goalie Brian Boucher's stick side nearly 5 minutes into the game, on a feed from Steve Downie after the puck bounced off the board.
Zherdev, one of the players signed with the money saved from shedding Gagne's $5.25 million salary, tied it a little more than 2 minutes later off an assist from James van Riemsdyk.
Tampa Bay made it 2-1 in the second period when Moore backhanded a rebound through Boucher's pads.
Kubina scored early in the third, and Philadelphia pulled within a goal midway through the period, when Briere wristed a shot past Dan Ellis.
Boucher, making his second start, stopped 21 shots. Ellis had 24 saves for Tampa Bay.
NOTES: Gagne, a first-round pick in the 1998 draft, played 664 games for the Flyers. He scored 259 goals, including two 40-goal seasons. He hasn't recorded a point in his first three games with Tampa Bay.