Jeff Schlupp's superb strike 11 minutes from time sealed a first league win in 10 matches for Nigel Pearson's men and saw them replace Wanderers in the play-off positions.
Leicester made the worst possible start falling behind in the third minute to David Ngog's penalty.
However, two goals in as many minutes just before half-time turned the game on its head. Chris Wood's 39th-minute penalty brought the Foxes level before Lloyd Dyer put them ahead in emphatic fashion after 41 minutes.
Darren Pratley levelled things up again midway through the first half but Schlupp had the final word, despite some intense late pressure from the visitors.
Leicester conceded a last-minute penalty to draw with Birmingham on Friday night and they conceded another after just 75 seconds when captain Wes Morgan tripped Lee Chung-yong.
As he did with Chris Burke's equaliser four days ago, Kasper Schmeichel dived the right way but Ngog's spot-kick was right in the bottom left-hand corner and found the back of the net via the post.
The game, and Leicester's season, then turned on its head in the space of two minutes.
Dyer's quick feet left Danny Butterfield in a tangle and the recalled defender tripped his man, leaving referee Eddie Ilderton with no choice but to point to the penalty spot.
Wood stepped up to take it and sent Adam Bogdan the wrong way with his spot-kick, stroking the ball into the bottom left-hand corner.
In the 41st minute the Foxes were ahead. Wood did brilliantly to draw the attention of three defenders before finding Dyer with a reverse pass. Dyer's first touch took him into the penalty area and with his second he crashed a left-foot past Bogdan and into the net off the underside of the crossbar.
Craig Davies replaced Josh Vela after 56 minutes and within four minutes of his introduction the striker struck a post with a dipping effort from 25 yards out.
Bolton's pressure finally told after 71 minutes when Pratley swept home substitute Sam Ricketts' low cross from the right.
However, Schlupp restored Leicester's lead with a sweetly-struck left-foot volley from the edge of the box.
Bolton kept coming forward and Schmeichel tipped over a header from Davies before Wanderers skipper Zat Knight glanced a header wide as the Foxes held on.