Turner racked up 70 yards.
Matt Ryan went 28-for-42 passing for 291 yards with a touchdown for the Falcons (2-2).
Matt Bryant went 3-for-3 on field goal tries for the victors.
Atlanta, however, had to sweat out the game's final drive as Seattle drove for the go-ahead score.
Tarvaris Jackson (25-of-38, 319 yards) moved the Seahawks from their own 15-yard line to the Atlanta 45 with 22 seconds left but Sidney Rice was whistled for a false start, setting them back to midfield.
Two plays later, Steven Hauschka tried a 61-yard field goal that would have won the game, but it fell short.