"The run game was huge," Wentz said. "It was good to get Ryan the ball, feed him the rock and he was running angry. That makes my job easier."
Mathews ran in from the 5 and also converted the 2-point conversion for a 21-15 lead with 7:14 left in the game.
Jones, sporting fashionable cleats to support the NFL's Salute To Service, had 10 catches for 135 yards.
"They outdid us in all phases," Falcons coach Dan Quinn said. "We had our opportunities and we didn't nail them. We had the lead and couldn't close it."
Mathews had just nine carries combined in the past two games while 33-year-old Darren Sproles was featured. But coach Doug Pederson made a point to establish the run right away. Mathews carried seven times for 34 yards on the first drive, taking it in from the 4 for a 7-0 lead.
Rookie Wendell Smallwood had 70 yards rushing and Philadelphia finished with a season-high 208 on the ground.
"That's an explosive offense and I felt we had to possess the ball and running game had to be a factor," Pederson said.
Ryan was 18 of 33 for 267 yards, one TD and one interception.
Copyright 2016 by The Associated Press