Tampa Bay's misery continued in the second half as Devin Hester scored the first of his touchdowns by rushing over from 20 yards out.
Hester was far from finished, and he extended Atlanta's advantage even further by returning a punt with a 62-yard run, allowing Matt Bryant to convert for the fifth of his eight extra points.
It was a party atmosphere inside the Georgia Dome for the Atlanta supporters as Ryan took advantage of a weary Tampa Bay defence to fire a pass to Jones, who collected for his second score of the night.
The Falcons were still dominating in all areas, with Steven Jackson rushing over from two yards moments after the Bucaneers had fumbled the ball for the sixth time.
Before the end of the third quarter, the gap between the two sides was stretched to 56 points when Antone Smith side-stepped challenge after challenge to rush 38 yards for his side's eighth touchdown.
Atlanta took their foot off the gas in the final quarter as Ryan was given a well-deserved rest, and Tampa Bay managed to reduce the deficit on a disappointing evening.
Mike Glennon, on as quarterback for the struggling McCown, hit the hands of Vincent Jackson with just under nine minutes remaining as Tampa Bay finally troubled the scoreboard.
However, the night would belong to the Falcons as they recorded their second win of the season.