The game-deciding kick came after the Steelers were able to retain possession of the ball on a confusing officials' ruling following a Ben Roethlisberger fumble.
The Steelers' signal-caller went 19-of-27 passing for 302 yards and two touchdowns for Pittsburgh (5-1), winners of five straight against Miami.
Hines Ward hauled down seven passes for 131 yards and a score for Pittsburgh.
The Dolphins (3-3) benefited from 257 passing yards by Chad Henne, who tossed a touchdown and went 23-of-36 through the air.
2014: The Year in Music [PHOTOS]