Ackley singled with one out off Alfredo Aceves (0-5), went to second on Miguel Olivo's single and came home with the decisive run when Figgins' flew out to right field, beating Cody Ross' wide throw to the plate.
Shawn Kelley (2-2) collected the win with a scoreless top of the 11th for Seattle, which bested Boston for the second time in their four-game set.
John Jaso drove in two runs for the winners.
Boston tied it in the seventh when Will Middlebrooks scored on catcher Olivo's passed ball.
Adrian Gonzalez went 3-for-5 with a run scored for the Bosox.