The Falcons had to settle for three Matt Bryant field goals and a 9-3 lead at halftime, but Ryan threw a 20-yard touchdown pass to Roddy White in the third period.
Backup Atlanta quarterback Dominique Davis added a 39-yard scoring toss to Tim Toone in the final quarter.
Atlanta won its first exhibition game in three tries.
Miami rookie Ryan Tannehill, named the Dolphins' starter for the regular season, completed 11-of-27 passes for 112 yards and an interception. The Dolphins remained winless in exhibition action.