Either 2009 when they swept both Baltimore & Pittsburgh, or early 2010 when they beat Baltimore at home. I think those games are usually "big games" for the Bengals, even early in the season.
I think it was the Chiefs game late in 2009 that they needed to win in order to win the division & they won it. The Chiefs weren't contenders, but it was a "big game" for the Bengals.