Beck, who came to Baltimore in free agency from Miami this season, played the entire exhibition game while starter Joe Flacco rested for next weekend's season opener against Kansas City.
The backup quarterback completed 16-of-28 for 232 yards. He hit Jason Cook with a 5-yard scoring pass in the opening period and threw a 15-yarder to Eron Riley in the fourth quarter.
Steven Hauschka added field goals of 33 and 46 yards, helping the Ravens complete a 4-0 exhibition season.
Atlanta's lone score came on Jason Elam's 45-yard field goal in the second quarter.
The Falcons went 2-2 in the pre-season and will start their campaign at home against Miami.