The one-time England international netted his sixth spot-kick of the campaign and his fifth in his last five Sky Bet Championship games as the in-form Foxes made it 13 points from their last five matches.
After a lively and even opening 45 minutes it was Nugent, their two-goal hero on Saturday, who broke clear of the offside trap to tee up Lloyd Dyer to break the deadlock.
And 11 minutes later he continued his impressive goalscoring form from the spot after Ritchie De Laet was fouled.
Referee Brandan Malone then awarded his second spot-kick of the half which saw Yeovil substitute James Hayter set up a nervy finale.
The Glovers came into the clash without a league point or even a goal in Somerset since clinching a historic promotion to the second tier but this was not a display from a side short on confidence.
Ed Upson was the first to threaten in an end-to-end encounter but De Laet just did enough to knock Saturday's goalscorer off his stride as he went to convert Andy Williams' clever pull-back.
Two minutes later fellow defender Luke Ayling timed his header to perfection as Wes Morgan stretched to meet Anthony Knockaert's inviting cross at the back post.
Andy King was making his 200th league start and after a clever flick his volley was nowhere near troubling international team-mate Wayne Hennessey.
Dyer and Vardy both blazed wide when well placed before Kasper Schmeichel was called into action for the first time in the 26th minute.
Joel Grant's curling cross forced the big Dane into a diving stop and when when the ball fell to Upson the former Ipswich trainee just could not get enough power on his low effort to break the deadlock.
Having scuffed the final chance of the opening 45 minutes at Hennessey Knockaert was inches away from an eye-catching opener three minutes after the break when he bent a first-time left-footed curler past the post.
The Foxes continued to look a threat on the break and it was a rapid counter attack which saw them open the scoring in the 54th minute.
Nugent flew down the left wing and his low centre was finished into the bottom corner for Dyer's third of the season.
A thumping first-time half-volley from Williams was right at the diving figure of Schmeichel and Duffy headed just wide from a corner as Gary Johnson's men looked for an swift response.
But just seconds later Dan Seaborne gave away a penalty for the second successive home game.
The former Southampton defender fouled De Laet, who had cut inside having been slipped in by Knockaert, and Nugent did the rest.
And Leicester should really have been celebrating again in the 67th minute when Vardy raced down the right flank and found Dyer on the penalty spot but he put his effort into the away end.
A set-piece straight off the training ground saw Madden fire a free-kick wide before their run without a league goal on home soil, stretching back five games to May, was finally broken.
Liam Moore tripped Upson and Hayter found the bottom corner from the spot with five minutes remaining but Leicester, and their in-form frontman, were not to be denied.
- Sports & Recreation
- Lloyd Dyer
- Ritchie De Laet
- James Hayter
- Andy Williams