Keller tied the game 4-4 at 19:25 of the third period, cutting in from the left boards and lifting a backhander over Samuel Ersson's glove from in tight. He then scored the game-winner with a snap snot from the slot off a pass from Dylan Guenther.
JJ Peterka, Lawson Crouse and Barrett Hayton scored, and Nick Schmaltz and Guenther each had two assists for the Mammoth (26-20-4), who extended their point streak to eight games (7-0-1) and finished 5-1-1 on a seven-game homestand. Keller also had an assist, and Karel Vejmelka made 25 saves.
Christian Dvorak scored twice and had an assist, and Cam York and Bobby Brink had goals for the Flyers (23-17-9), who have lost seven of eight (1-5-2). Trevor Zegras and Jamie Drysdale each had two assists, and Samuel Ersson made 22 saves.
York gave Philadelphia a 1-0 lead just 30 seconds into the first period. Dvorak got a piece of Travis Sanheim's shot from the slot that was initially stopped by Vejmelka, but the rebound was buried by York from the bottom of the right face-off circle.
Dvorak made it 2-0 at 4:30 when he took a pass from Konecny in stride into the offensive zone and went backhand-forehand to tuck the puck around Vejmelka's right pad.
Brink pushed the lead to 3-0 on the power play 58 seconds into the second period. He beat Utah forward Jack McBain
to the rebound from a Zegras shot at the left of the crease and tapped it in.
Peterka cut the deficit to 3-1 at 5:35 after the puck came loose out of a scrum to the left of the net and he scored into an open net from in front.
Crouse brought the Mammoth to within 3-2 just 36 seconds later at 6:11, taking a feed from Nick Schmaltz and beating Ersson's glove with a snap shot from the slot.
Dvorak put Philadelphia back up 4-2 with a power-play goal at 10:28. He sent a wrist shot from the right circle off the rush and knocked his own rebound in under the stick of Vejmelka for his second goal of the game.
Hayton made it 4-3 on the power play at 12:47 of the third period after Guenther's wrist shot from the left circle deflected off him in front.