The Thrashers rallied from a 3-1 deficit to hand Philadelphia its first loss when leading after two periods. The Flyers were 22-0.
Ilya Kovalchuk and Rich Peverley also scored for the Thrashers, and Evander Kane set up both of Slater's goals with nifty wraparound passes.
Atlanta moved one point ahead of the Flyers, who entered the night in a four-way tie for sixth place in the Eastern Conference. Claude Giroux, Arron Asham and Dan Carcillo had goals for Philadelphia, 11-5-1 in its last 17 games.
This was a rare victory for the Thrashers, who have been dominated by Philadelphia during their 10-year history. The Flyers are 29-5-4 against Atlanta, including 14-2-3 at home.
Trailing 3-1, the Thrashers quickly went to work in the third. Kovalchuk scored his 31st goal just 29 seconds in to cut it to 3-2. He picked up a loose puck off a faceoff and shot one over goalie Ray Emery, who was sprawled on the ice.
A few minutes later, Peverley slipped by the defense, took a long pass from Pavel Kubina and scored a breakaway goal to tie it at 3.
Then Kane skated down the left side, went around the net and placed a perfect pass on Slater's stick. Slater slipped it in for a 4-3 lead with 6:32.
Kane and Slater hooked up on a similar play to put Atlanta up 1-0 late in the first.
Atlanta's Johan Hedberg stopped 34 shots. He ranged far out of the crease and poked the puck away from a streaking Simon Gagne with 3:51 left. Hedberg lost his mask during the collision and his sweater slipped over his head, drawing laughter from the crowd.
The Flyers scored three goals in a span of 6:25 in the second period to take a 3-1 lead. Giroux tied it at 1 with an unassisted goal following some fancy stickwork. Giroux skated around a defenseman, deked Hedberg and put a shot in from just behind the net.
Giroux then made a perfect cross-ice pass to Asham, who lifted a shot past Hedberg to give Philadelphia a 2-1 lead.
Carcillo extended the lead to 3-1 when he poked one past Hedberg off a crisp pass from Ian Laperriere along the boards.
Minutes earlier, Hedberg stoned Scott Hartnell on a breakaway. The rebound kicked right back to Hartnell, who missed an open net. Kovalchuk might be playing out his final days with the Thrashers. He could become an unrestricted free agent after the season, so it is possible he will be dealt before the NHL trade deadline on March 3.
There have been rumors the Flyers might be interested in acquiring the three-time All-Star, but it is unlikely they could fit his $6.4 million salary under the cap.
NOTES: Gagne played his 634th game, moving into 11th place on the Flyers' career list. ... Asham has 10 points in his last 12 games. ... The Thrashers beat Philadelphia 1-0 on Nov. 28.
