It was very much high fives all-round for Nigel Pearson's in-form side as they maintained their recent good form.
Nugent's fifth league strike of the season and Richard Foster's own goal secured the Foxes' fifth straight victory - following excellent away wins at Middlesbrough and Huddersfield - and also brought their fifth win in a row at their King Power Stadium home.
The result took the Midlanders top of the table prior to Cardiff's televised late afternoon clash at Ipswich, but the success did not come without a cost, with the Foxes losing three players through injury.
Paul Konchesky was forced to withdraw at the break, Jamie Vardy hobbled off in the 51st minute, and then after 63 minutes Republic of Ireland international defender Sean St Ledger also picked up a knock.
The Robins, who had chalked up a league double over Leicester last season, had almost snatched the lead inside the first minute, Jody Morris meeting Sam Baldock's cross but his six-yard header was saved by Kasper Schmeichel.
The Foxes responded well and after eight minutes a left-foot shot by Lloyd Dyer was tipped over the crossbar by City goalkeeper Tom Heaton.
The visitors, the second-highest scorers in the Championship going into the contest, with 18 goals, had certainly not come to sit back and defend in the early stages and following a corner from Morris into the heart of the Leicester box, Liam Fontaine sent a 10-yard shot wide of the right-hand upright.
Leicester's former England striker Nugent headed over from six yards out in the 28th minute, but he made amends just 60 seconds later. Vardy's long ball from the back caught the Robins rearguard napping and Nugent raced through one-on-one with Heaton and drove a low right-footer into the bottom corner.
Heaton kept City in the hunt with smart saves from both Nugent and French ace Anthony Knockaert in the space of a few seconds in the 36th minute.
The Robins had lost their record as being the only Championship team not to have gone in trailing at half-time - and boss Derek McInnes decided to replace Baldock with Steve Davies in the 59th minute.
Fontaine fluffed a good chance to bring City level in the 71st minute, the big defender heading an inswinging corner from Morris over the top from six yards, and that miss proved costly as the Foxes forged further ahead on 74 minutes, Andy King's left-wing cross being headed into his own goal by the unfortunate Richard Foster.
It brought up Leicester's 50th goal against their west country opponents and was enough for them to chalk up their fifth straight league win for the first time since February 2011.
As for the Robins, they have now failed to win six of their last seven league outings.