Neil Warnock's players fought back after conceding a goal inside four minutes to thoroughly outplay a City side hampered by the dismissal of Callum Davidson, snatching victory in the fifth minute of injury-time when Carl Asaba scored his second goal of the match from point-blank range.
A fiercely competitive first 45 minutes had seen two controversial goals - both allowed to stand by referee Andy D'Urso - but United's outstanding second-half display, when the Foxes were rarely in the game, should now ensure their involvement in the play-offs.
Muzzy Izzet's goal against Brighton on Saturday had set Leicester up for the 2-0 victory which finally sealed promotion to the Barclaycard Premiership, but the midfielder was missing at Bramall Lane with a gashed knee.
Manager Micky Adams brought in striker Brian Deane to replace the Turkish international, moving Trevor Benjamin onto the left wing, and the switch could hardly have worked any better as the Foxes grabbed the lead in the fourth minute.
Benjamin, who appeared to catch Peter Ndlovu with his elbow during the build-up, curled a cross to the far post where Brian Deane was left unmarked to hammer a low shot across goalkeeper Paddy Kenny and into the net.
The early strike unsettled United but in the 15th minute they pulled themselves level following an excellent run from Tonge.
The former Manchester United player picked up the ball just inside the Leicester half and dribbled into the box before a precise cut-back found Carl Asaba, who forced a shot through Ian Walker's legs.
The goal angered City, who claimed the ball had gone out for a throw-in prior to Asaba's finish, and Andy Impey was booked for dissent by D'Urso.
City's James Scowcroft and United's Peter Ndlovu both hit the post before Davidson - booked in the first half for a foul on Michael Brown - was dismissed in the 56th minute after clattering the same player with a needless challenge.
And after Steve Kabba had headed a wonderful chance wide in stoppage-time, Shaun Murphy's knock down was clipped over the line by Carl Asaba.