كتب : وكالات
The 90 minutes ended scoreless and the match went to extra-times.
Mido stuck the winner five minutes before time but his shot was deflected and keeper Paddy Kenny failed to retrieve the rebound and put it in his own goal.
The 24-year old striker was in Boro's starting line up for the first time this year and put a lot of pressure on Sheffield's defense.
Middlesbrough will face Cardiff City in the quarter finals.