Liam Lawrence had given the home side the lead seconds before half time with a deflected goal. City had a goal disallowed and a penalty claim turned down before substitute Barmby pulled it back to 1-1 two minutes into stoppage time at the end of the game.
City remain 4th from bottom as Barnsley, Leicester and QPR all achieved wins today.
However, the Tigers go a point ahead of Leeds, who lost 1-0 at Southampton. Leeds, reduced to ten men in the first half as Alan Thompson was shown a red card, conceded 6 minutes from time as substitute Bradley Wright-Phillips scored for the Saints.
They remain three points ahead of Southend, who also lost to a late goal. Barry Hayles got the winner for Plymouth in the 90th minute as they beat the Shrimpers 2-1 at Home Park.