Despite each team tallying goals in the middle frame, the Oilers continued to dominate in the shot column with a 35-18 advantage through 40 minutes.
The penalty concerns continued for the Oilers early in third as Lucic was sent to the sin bin for a high stick, but there was no concern for Kassian as he broke free shorthanded and buried his sixth of the season to put his team up 4-2 at the 4:07 mark.
Unfortunately, the two-goal lead didn't last long as the Flyers managed to rebound and score their third PPG of the night just 27 seconds later courtesy Travis Konecny at the side of the net.
The parade to the penalty box continued for the Oilers as it was Kassian's turn to sit after a high stick and the Flyers found their fourth PPG of the game from Wayne Simmonds to tie the game at 11:02.
Talbot made a series of miraculous saves in the final minute to send the teams to overtime before Patrick pounced on a loose puck and flicked it top corner for the game-winner.
"It's a frustrating way to lose a hockey game," said Talbot, who made 34 saves. "We played so well five-on-five, but we just kept giving their power play opportunities and they kept making us pay. Our penalty kill, starting with me tonight, cost us the game."
"We did a lot of good things, but our penalty kill has got to be better," added defenceman Darnell Nurse. "Any time you give up four goals, you shoot yourself in the foot pretty good. We found a way to get a point and had a lot of positive things to build off, especially five-on-five."
As the number in the games played column keeps getting higher, an effective PK becomes increasingly crucial, said Hitchcock.
"If you don't kill penalties, it's a tough time of year," he said. "You've got to be able to do it if you're going to win hockey games in the last half of the season & we haven't been able to do it for a little while, not to the level you have to be if you're going to be good at it."
Next up, the Oilers will conclude their weekend back-to-back with another matinee on Sunday as they head north to Montreal for a 12 p.m. MT matchup with the Canadiens.