City earned a rare away victory against an Ipswich side who had not lost at home since the start of January.
An entertaining encounter between two sides guilty of underachieving this season saw Jason Scotland break the deadlock in the 43rd minute, with the veteran striker, 33, returning to the fold to make his 18th league start of the campaign for Town having waived his right to a bumper new deal if he makes 19.
But Ben Marshall levelled for the Foxes on the stroke of half-time with a long-range free-kick which caught out Ipswich goalkeeper Arran Lee-Barrett.
Leicester, sparked by half-time substitute Paul Gallagher, were much improved immediately after the restart and David Nugent, with his ninth goal in 10 games against Ipswich, headed the game's winner just before the hour mark.
The victory keeps Nigel Pearson's side in ninth place but now just three points off the top six with four games remaining, while mid-table Ipswich were left nursing only their second defeat in 10 games.
The hosts - showing four changes from Saturday's goalless draw at Derby, including a first start in England for January signing Ryan Stevenson - enjoyed the better of the opening quarter against an unchanged Leicester.
Scotland forced a solid save from Kasper Schmeichel, who produced an even better stop to tip Grant Leadbitter's 30-yard free-kick around a post.
Jermaine Beckford fired well over when he really should have done better for the Foxes while Scotland sent a decent effort off target at the other end.
Two late blocks denied Scotland and Josh Carson just before the half-hour mark, with Town making almost all of the running.
Beckford was guilty of poor finishing for a second time as his tame shot failed to really test Lee-Barrett, who was soon forced into action by Nugent as the visitors threatened for the second time in as many minutes.
Schmeichel was again called upon to keep out Stevenson, providing the hosts with their eighth corner of the first half.
And Town finally broke the deadlock two minutes before the break, Scotland receiving the ball from Lee Bowyer before turning his man and finally beating Schmeichel with a cool finish.
But no sooner had they done so than Leicester levelled, Marshall's fierce 35-yard free-kick deceiving Lee-Barrett, who really should have done better.
Foxes boss Pearson brought on Gallagher and Andy King at the break and the former almost inadvertently supplied an immediate return.
His teasing cross was fired towards his own goal by Ipswich skipper Carlos Edwards, whose blushes were spared thanks to a great stop from Lee-Barrett, making up for his earlier mistake.
King was booked for an alleged dive at the feet of Lee-Barrett, who again did well to keep out Gallagher.
But he was beaten by Nugent's header in the 58th minute having initially palmed out the striker's effort.
Having taken the lead Leicester did a great job of closing out of the game, with Schmeichel not forced into a save of note over the remaining half-hour.