Dan Bailey kicked his seventh career game-winning field goal, booting a 40-yarder as time expired as grieving Dallas posted its fourth win in five contests.
Tony Romo connected with Dez Bryant on a 27-yard touchdown and DeMarco Murray had a 1-yard rushing score for the visiting Cowboys (7-6), who were playing one day after the death of practice-squad linebacker Jerry Brown.
Romo completed 25 of 43 passes for 268 yards, and his scoring strike over the middle to Bryant cut Cincinnati's lead to 19-17 with 6:44 remaining in the fourth quarter.
After forcing the Bengals (7-6) to punt, Dallas pieced together a 13-play, 50-yard drive before Bailey split the uprights to end the game.
Signed on Thursday after Mike Nugent suffered a calf injury in practice, Josh Brown drilled field goals of 25, 33, 25 and 52 yards for the Bengals.
GAME NOTEBOOK: A moment of silence was observed for Brown, who was killed in a pre-dawn accident on Saturday. Bond was set at $500,000 on Sunday for Dallas DT Josh Brent, who was charged with intoxication manslaughter in the accident. ... WR Andrew Hawkins did the leg work on Cincinnati's first score, taking a quick shovel pass from Andy Dalton before racing around the right end for an 8-yard touchdown. The score was Cincinnati's NFL-leading sixth on its opening drive. ... Bengals RB BenJarvus Green-Ellis rushed for 89 yards, stopping his streak of three straight games going over the century mark.