The lead was extended with just over three minutes remaining in the opening quarter as Julio Jones collected another incisive pass from Ryan before running over.
Tampa Bay's struggles continued, though, and they were 21-0 behind at the end of the first period when Kemal Ishmael intercepted a pass from Josh McCown before scoring his side's third touchdown to the delight of the home fans.
Atlanta's domination continued in the second quarter as Devin Hester registered his first touchdown by rushing over from 20 yards.
There would be no response from the Buccaneers, and the disappointing night was made even worse when Hester collected a Michael Koenen punt, before avoiding his rivals in a 62-yard return.
Matt Bryant stepped up to convert the extra point for the fifth time as the Falcons stormed into the interval on top form.