The home side made a storming start when top scorer David McGoldrick scored with less than two minutes on the clock.
But the Foxes responded brilliantly after the break with Nugent twice capitalising on the flying Lloyd Dyer's build-up play to make it an amazing 13 goals in 12 matches against the Suffolk side.
Ipswich caught their high-flying visitors cold after just one minute and 45 seconds. There appeared to be little danger when McGoldrick picked up the ball about 25 yards out, but the in-form striker's low shot went under a bemused Kasper Schmeichel for his seventh of the season.
Leicester looked to hit back instantly but Nugent's shot from an acute angle went wide.
The visitors, second from top at kick-off, almost contrived to concede a second with only eight minutes played when Paul Konchesky's back pass was woefully under-hit but Schmeichel smothered McGoldrick's side-footed shot.
Leicester came closest to levelling with three minutes to play in the first half when Andy King met Danny Drinkwater's corner and Dean Gerken had to be alert to tip over.
But it was Ipswich who ended the half on top, Daryl Murphy and Paul Anderson unable to take advantage of half chances before Schmeichel fisted clear Ryan Tunnicliffe's cross-shot.
Manchester United loanee Tunnicliffe almost doubled Town's advantage moments after the restart but his low shot was well held by Schmeichel after good build-up play by Murphy and Jay Tabb.
But in the 51st minute Leicester were level with a cracking goal, both in terms of build-up play and execution. Dyer's run down the left saw his cross teed up by Jamie Vardy and Nugent buried a 12-yard shot into the corner.
Town were on the ropes and Dyer's cross almost again provided dividends but Vardy's powerful half-volley was blocked by the chest of home goalkeeper Gerken.
It mattered not as Dyer burst onto Drinkwater's perfect through ball to round Gerken and tee up Nugent for his and the Foxes' second to complete a dramatic six-minute turnaround.
Shell-shocked Ipswich looked to fight back and substitute Paul Taylor's teasing cross was headed just wide by Luke Chambers in the 73rd minute.
Within 60 seconds, it was the visitors who almost extended their lead when some great work by Vardy saw a low cross clipped just over by the advancing Dyer.
Ipswich huffed and puffed but never looked likely clawing back an equaliser, McGoldrick's speculative long-ranger curler was the closest they came.
At the other end, Nugent came close to a hat-trick but narrowly missed the far post after breaking clear down the left.