Nugent netted for the first time in 17 matches with eight minutes remaining to give the Foxes a 1-0 lead to protect in Sunday's second leg at Vicarage Road.
It looked like Nigel Pearson's side might be left to rue their failure to take the chances they created, particularly during the first half.
But Watford will also be disappointed not to have scored, with Ikechi Anya and Matej Vydra spurning one-on-one chances in each half.
Leicester started brightly, getting at their opponents from the off and cheered on by a season-high crowd of 29,560 at the King Power Stadium.
Nugent flicked a third-minute cross from Lloyd Dyer goalwards but it lacked the power to beat Manuel Almunia and the Spaniard, fit again after a hamstring injury, smothered the ball.
Almunia was then in the right place when Ritchie De Laet's near-post header from Matty James' corner stuck in his midriff.
Eighteen minutes of almost relentless Leicester pressure was broken when a mistake by makeshift left-back Jeff Schlupp presented Watford with the best opening of the match.
Schlupp's miskick midway inside his own half allowed Anya a clear run at goal but Kasper Schmeichel spared his blushes.
Schlupp's clearance only went as far as Almen Adbi but Schmeichel got down quickly to make a second parrying save before De Laet cleared the loose ball to the safety of the stand.
The episode gave Zola's team a foothold in the game and Marco Cassetti's 30-yard effort worried Schmeichel enough for the Dane to fling himself to his left as the shot just missed the top corner.
Dyer and Nugent combined again after 27 minutes. This time Leicester's leading scorer made a solid connection but he steered his side-foot effort a yard wide when he really should have broken his long run without a goal.
Anya had a goalbound shot strike Andy King just after the half hour mark as Watford were beginning to look threatening.
But the visitors had Almunia to thank as they went into half-time all square.
The Hornets' captain blocked Anthony Knockaert's near-post shot after the tricky winger had beaten Cassetti in a foot race and then cut inside Daniel Pudil's sliding challenge.
Watford spurned another golden opportunity on the hour mark.
Cassetti's crafted pass with the outside of his foot found Vydra in space on the edge of the box but the Championship's player of the year failed to add to his 20 league goals this season and scuffed his shot tamely at Schmeichel.
The Czech Republic international then hit a shot with some force from the left side of the area that Schmeichel had to push away before Nugent broke t5he deadlock.The Leicester frontman headed home Knockaert's free-kick in the 82nd minute for his 15th goal of the season, having been stuck on 14 since scoring the winner in a 2-1 home win over Wolves on January 31.
|Leicester City||Team Statistics||Watford|
|0||1st Half Goals||0|
|5||Shots on Target||6|
|4||Shots off Target||8|
|51.8||1st Half Poss.||48.2|
|53||2nd Half Poss.||47|