Rookie Sean Monahan scored the lone goal of the game for the Flames (14-20-6), who have now lost three straight after dropping a pair of 2-0 decisions at home to the Edmonton Oilers on Friday and the Vancouver Canucks on Sunday.
Starting his fourth straight game for the Flames, Reto Berra made 17 saves in a losing cause.
The game marked the debut of forward Kevin Westgarth, who was acquired by the Flames from the Carolina Hurricanes on Monday in exchange for centre Greg Nemisz. Westgarth played on a line with Joe Colborne and Brian McGratton.
Streit then put the Flyers up 1-0 at 3:15 of the first when his let go a wrist shot from the point that found its way into the top corner over the outstretched glove of Berra, who was screened by Simmonds and Hartnell on the play.
Shortly after Emery stood his ground to stop a shot from the slot off the stick of Monahan, Berra made a pad save at the other end of the ice to deny a scoring chance by Steve Downie.
The Flyers continued to pour on the pressure as Streit rang a shot off the post before Schenn appeared to score to put Philadelphia up 2-0, but the goal was waved off because Hartnell made contact with Berra after taking the initial shot on goal.
Monahan tied the game at 1-1 with his first goal in seven games at 14:30 of the second. Monahan skated down the left wing into the Philadelphia zone on a 2-on-1 with Lee Stempniak. Instead of passing, Monahan fired a shot to the far side into the net over Emery's left pad to end Calgary's goalless drought at 159 minutes 35 seconds.
Jakub Voracek then had a chance to regain the lead for the Flyers, but he fell down in the slot and Berra poke checked the puck out of harm's way.
With 1:29 left in the second, Schenn put Philadelphia back up by one when he spun and fired a shot from the slot past Berra.
Hartnell added an insurance marker for the Flyers at 10:14 of the third when he tipped Luke Schenn's point shot past Berra. Brayden Schenn also drew an assist on the goal for his third point of the game.
Coburn rounded out the scoring with a late empty-net goal while the Flyers were killing a penalty.
Notes: Calgary now has an all-time record of 12-8-3 on games played on New Year's Eve. Heading into Tuesday's game, the Flames had won the last six times they have played on New Year's Eve, including a 3-2 win at home over the Colorado Avalanche on Dec. 31, 2010. … After playing 6:24 in the first period, Philadelphia forward Matt Read left the game with upper-body injury and didn't return. … The Flyers have now won five straight games at the Saddledome against the Flames.