Flyers forward Max Talbot, who had his nose bloodied after being hit by Benoit Pouliot and going headfirst into the boards in the second-period, said he was "really concerned" that the goal would stand.
"We caught a break there, because sometimes they call it for your side, sometimes they don't," said Talbot, who returned to the ice in the third period and said afterward he wasn't sure if he would need surgery on his nose. "It's such a tight play, and I feel like it was kind of the break we needed."
Before Thursday, the Flyers had been outscored, 12-2, in the third period of games.
Coburn scored on a point drive after a feed from Matt Read. Wayne Simmonds set up a screen in front.
About two minutes later, the Rangers (2-6) appeared to tie the score on Miller's power-play goal with Claude Giroux in the penalty box for hooking. But the replay officials ruled otherwise.
"I was talking to my friend upstairs" during the review, Giroux said.
"I didn't necessarily think I kicked it," said Miller, who added: "It caught me off guard. I didn't even know it went in until everybody was [celebrating]."
The Flyers improved to 2-7. They have scored 13 goals - two by Coburn - in nine games.
"Everybody's trying to pull in the same direction here, and it's a matter of just putting it all together," said Coburn, who has the game-winners in both Flyers victories. "We've got a lot of good pieces here."
In each of their nine games, the Flyers have entered the third period tied, ahead by a goal, or down by a goal.
The teams were deadlocked at 1-1 heading into Thursday's third period.
The Flyers appeared to be handed a gift from the hockey gods because Rangers goalie Henrik Lundqvist and forwards Ryan Callahan and Rick Nash missed the game with injuries. Cam Talbot replaced Lundqvist and made his NHL debut.
Read's first goal of the season, a shorthanded tally midway through the opening period, gave the Flyers a 1-0 lead. He had 12 goals and 12 assists in 15 collegiate games against Cam Talbot, a stat he didn't realize until PR director Zack Hill e-mailed it to him earlier in the day.
After reading it, "I kind of felt tonight might be my night," Read said.
Read pounced on Derick Brassard's turnover near the defensive blue line and scored on a breakaway, firing a shot through Cam Talbot's legs.
But with 1:04 left in the first period, Brad Richards scored the equalizer as his shot from an odd angle - near the boards and close to the goal line - deflected off Coburn's right leg and past goalie Steve Mason (30 saves).
The Flyers came close to snapping the tie in the second period, but long shots by Kimmo Timonen and Luke Schenn hit the post.
In his debut, Cam Talbot was solid, but the Flyers were not crisp, especially on their power play. They failed to convert on a five-minute man advantage that carried into the first two minutes of the third period. At that point, they were 0 for 4 on the power play for the night, and in a 1-for-25 skid in the last seven games.