Nick Bjugstad gave Florida a 1-0 lead in the shootout, and after Panthers goalie Roberto Luongo stopped Nick Cousins, Barkov ended it when he beat Flyers goalie Steve Mason between the legs with a wrist shot.
"I just wanted to score, nothing fancy," Barkov said. "I like to shoot five-hole. (It's) just confidence when you score a goal in a shootout, then you know what works, what doesn't work. I scored last time when I shot five-hole; now I had a lot of confidence to score that way again."
The Panthers are 7-3 in the shootout; the seven victories are the most in the NHL. Barkov has scored the deciding goal in four of the wins.
Video: PHI@FLA: Gostisbehere beats Luongo to tie it late
Florida made it to the shootout after killing a penalty in overtime.
"Our guys did a great job there on the PK in overtime," said Luongo, who made 22 saves. "Lot of huge blocked shots, guys sacrificing their bodies like that. We haven't seen much of that this year, but it was great to see in a time like that guys laying out and making some huge blocks."
Reilly Smith scored two goals, Jonathan Huberdeau and Barkov each had one, and Jaromir Jagr had two assists for Florida (38-21-9), which is one point behind the Boston Bruins for first place in the Atlantic Division with two games in hand.
"It was up-and-down hockey, but I felt even if they had a one-goal lead, we could come back," Jagr said. "And I think they thought the same way. It looked like it was going to be overtime all night long. Whoever gets the lead, the other guy is going to tie anyway."
Michael Raffl had a goal and an assist, and Cousins, Ryan White and Shayne Gostisbehere scored for the Flyers (32-23-12), who had a three-game winning streak end and lost for the second time in eight games (6-1-1). Sam Gagner had two assists.
Video: PHI@FLA: Smith scores twice against the Flyers
Mason, who started Friday when the Flyers defeated the Tampa Bay Lightning 3-1, made 25 saves. He was pulled 6:46 into his first game at BB&T Center this season after allowing four goals on eight shots in a 7-1 loss Oct. 10.
Philadelphia is two points behind the Pittsburgh Penguins for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.
Although the Flyers were happy to take three points from their back-to-back against Tampa Bay and Florida, captain Claude Giroux bemoaned the missed opportunity in overtime.
"If you told me we were going to get three points this weekend, we would have taken it," Giroux said. "But we were in a situation to be able to get two points and at the end there two minutes of 4-on-3, I take responsibility for that one. I think we need to get it done. That's a really big point that we need to get."
Florida led 4-3 before Gostisbehere tied it with 1:55 left in the third period with a wrist shot from the right point that found its way past Luongo through a crowd. Gostisbehere, a native of South Florida who was playing his first game at BB&T Center, leads NHL rookie defensemen with 38 points.
"It was awesome," Gostisbehere said. "Of course, we wanted a better result at the end, but it was kind of a dream come true. You grow up watching all the games in this building, and then go out there and score a goal. It's pretty cool."
Video: PHI@FLA: Huberdeau buries Jagr's pass
Earlier in the third, the Panthers scored twice in 1:05 to take a 4-3 lead.
Barkov tied it 3-3 at 8:24 on the power play after taking a pass from Bjugstad at the left faceoff dot. Barkov held the puck before beating Mason with a low shot to the stick side.
Smith scored when he redirected Jussin Jokinen's backhand pass across the front of the net. Jokinen has two goals and 10 assists during his 10-game point streak, which matches his NHL career high.
Smith had four goals in two home games against Philadelphia this season.
"It seems to be working out," Smith said. "Wouldn't be bad if we played them a couple more times."
Raffl gave the Flyers a 3-2 lead at 1:28 of the third when he tipped Evgeny Medvedev's wrist shot from the point in front of the net from his knees.
Video: PHI@FLA: Barkov ties the game on the power play
Smith opened the scoring at 10:22 of the first period when he beat Mason on a 2-on-1 with a wrist shot high to the glove side.
Cousins tied it at 14:36 of the first after Gagner won a battle for the puck behind the Florida net. Gagner backhanded a pass to the front of the net that Cousins one-timed past Luongo.
White gave Philadelphia a 2-1 lead at 13:16 of the second period with a power-play goal. With Garrett Wilson in the penalty box for tripping, White deflected Gagner's redirection of Matt Read's shot from the point.
The Panthers tied it 18 seconds later thanks to a strong individual effort by Jagr. After skating into the Flyers zone against three defenders, Jagr kept control of the puck skating backward before dropping a pass that Huberdeau one-timed over Mason's left shoulder.
"That's my new move," Jagr said. "I want to show those kids before I retire, so I don't want to take it to the grave. He yelled for the puck. He's a goal-scorer now."
Video: PHI@FLA: Raffl tips the puck past Luongo
The Panthers honored members of their 1996 team, which reached the Stanley Cup Final in the third season in their history. Flyers assistant Gord Murphy played on that team.
Philadelphia defenseman Andrew MacDonald missed the game with a lower-body injury despite taking part in warmups. General manager Ron Hextall said MacDonald is day-to-day.
Goalie Anthony Stolarz was recalled from Lehigh Valley of the American Hockey League on Saturday to serve as Mason's backup with Michal Neuvirth sidelined by a stomach virus.
The Flyers host the Detroit Red Wings on Tuesday. The Panthers, who have won two in a row after a three-game losing streak, begin a three-game road trip Monday against the New York Islanders.
"We battled for those points," Florida coach Gerard Gallant said. "Philly came in here and played a real good game, so we're pretty happy to leave with two points. They had a great game against Tampa; we watched that. It was probably tough on them back-to-back. For us, it's a huge two points."
Video: Barkov's shootout winner lifts Panthers over Flyers