Rainey's score at the end of an eight-play, 67-yard drive broke a 17-17 deadlock and lifted the Steelers (3-3) to their second win in three games.
Pittsburgh rallied from 14-6 and 17-14 deficits in racking up its fifth straight win in Cincinnati.
Ben Roethlisberger completed 27-of-37 passes for 278 yards with a touchdown and an interception. Jonathan Dwyer rambled for 122 yards on 17 carries for the winners.
Andy Dalton was held to 105 yards on 14-of-28 passing efficiency with a score and a pickoff for the Bengals (3-4), who fell to 5-15 all-time against the Steelers.
BenJarvus Green-Ellis led Cincinnati's rushers with 69 yards on 18 carries.