The result leaves the Championship leaders eight clear of second-placed Derby, while Nigel Clough's Blades are now a point above the League One relegation zone
Nigel Pearson's promotion-chasers looked to be heading for a first defeat in 12 league matches after Jamie Paterson and Andy Reid had scored in quick succession for the hosts just before half-time to cancel out Jamie Vardy's 29th-minute opener.
And their task seemed even harder when Paul Konchesky was sent off for a challenge on Jamie Mackie just past the hour.
But with nine minutes left, Paterson turned from hero to villain when he brought down Danny Drinkwater in the box and, although veteran Kevin Phillips' spot-kick was missed, substitute Riyad Mahrez was on hand to follow up with the rebound as Leicester stretched their lead over second-placed Burnley to eight points.
Vardy had earlier opened the scoring for Leicester after 29 minutes, making the most of a defensive mix-up to score.
But Forest showed plenty of character to turn the match around with a quickfire double before the break.
First, Paterson was on hand in the 39th minute to nod home a cross after the visitors' defence had only partially cleared a corner, before Wes Morgan was adjudged to have brought down Mackie in the area and Reid stepped up to fire home the resulting penalty.
Leicester piled forward after the break and were unlucky not to grab an equaliser when David Nugent spurned what seemed a simple tap-in after the ball was squared across the box.
Their challenge appeared to have faded when Konchesky was sent off for a clash with Mackie but, with time running out, Drinkwater was felled and Mahrez provided the decisive contribution from Phillips' penalty.
Meanwhile, in League One, FA Cup heroes Sheffield United - who had beaten Forest last weekend - won 1-0 at Gillingham to move out of the relegation zone, with Conor Coady's goal four minutes before the break proving the winner.