It is the longest winning streak for the Flyers since they won 10 straight from Nov. 27-Dec. 14, 2016.
"Right now we're a confident team and it shows in how we handle ourselves throughout the game," Couturier said.
Connor McDavid scored his 30th goal and had an assist for Edmonton (23-24-4), which lost its fourth straight game (0-3-1). Zack Kassian had a goal and an assist, and Ty Rattie and Adam Larsson scored. Cam Talbot made 34 saves.
"Found a way to get a point, there's a lot of things we can build off, especially 5-on-5," Oilers defenseman Darnell Nurse said. "But as a penalty killer myself can't be letting the guys down by giving up four."
Kassian put the Oilers ahead 4-2 with a shorthanded goal at 4:07 of the third period, but the Flyers scored twice on the power play tie it, Konecny at 4:34 to make it 4-3, and Simmonds at 11:02 for a 4-4 tie.
Philadelphia entered Saturday 29th in the NHL on the power play at 14.1 percent but scored four with the man-advantage for the first time since Dec. 13, 2008, after going 2-for-2 in their 3-2 overtime win against the Boston Bruins on Thursday.
"We're starting to get a few bounces and they're coming to us and we're bearing down and putting them in," Simmonds said. "It's now winning games as opposed to losing us games."