One week after being held to one catch in a win at New Orleans, Jones had a 75-yard scoring catch late in the game as Atlanta solidified its early hold on the NFC South lead.
The totals by Ryan and Jones are the most ever allowed by Carolina.
Robert Alford's 30-yard interception return for a touchdown with 1:14 remaining clinched the win. Alford picked off another pass from Anderson to end Carolina's final possession.
The Falcons (3-1) began the day leading the NFL in scoring and total offense. They were rarely stopped by Carolina, even when pinned back close to their own goal line. They scored touchdowns after beginning drives on their 2- and 1-yard lines.
Copyright 2016 by The Associated Press