With Pittsburgh trailing 20-10 in the fourth quarter, Ben Roethlisberger (21-of-30, 216 yards, two TDs, one interception) connected on a 51-yard scoring pass with Mike Wallace, cutting the Steelers' deficit to three.
The Pittsburgh defense then stifled three consecutive Giants drives as Roethlisberger engineered a nine-play, 51-yard drive capped by Redman's go-ahead, 1-yard TD run.
Wallace made three grabs for 66 yards for the Steelers (5-3), who won their third straight.
The Giants (6-3), meanwhile, had their four-game winning streak snapped as Eli Manning was held to 10-of-24 passing for 125 yards and an interception.
Notable deaths of 2014 [PHOTOS]