Hester broke a league record with his 20th return for a touchdown - just one of many highlights in Atlanta's comprehensive triumph.
The Falcons stormed into a 21-0 lead at quarter-time and extended that to 56-0 at the final change before Tampa Bay finally scored.
But their two late touchdowns meant little as they slumped to their third loss in as many matches this season.
Matt Ryan threw for 286 yards and three touchdowns in the win while wide receiver Julio Jones caught nine passes for 161 yards and two touchdowns.
Harry Douglas, Jones and Kemal Ishmael entered the end zone in the first quarter as Atlanta started brightly.
And Hester took centre stage in the second quarter, scoring both touchdowns.
First came a 20-yard run before he made history with a 62-yard punt return that extended Atlanta's advantage to 35-0.
Hester moved past Hall of Famer Deion Sanders in the all-time list of career return touchdowns with his score.
Jones provided another Atlanta highlight in the third quarter, making a superb catch running back with the flight of the ball for a 40-yard touchdown.
Further scores to Steven Jackson and Antone Smith gave Atlanta a 56-point lead, meaning fourth-quarter touchdowns from Vincent Jackson and Danny Lansanah were of little consolation to the hapless Buccaneers.