A superb strike from James Justin had the Foxes ahead at the interval before Jamie Vardy headed home a second and then scored a fine solo goal to cement City's fifth victory in eight games across all competitions.
Manager Brendan Rodgers made seven changes to the side that beat Everton at Goodison Park in the Premier League on Saturday, with captain Jonny Evans making his first appearance for a month after an injury. Daniel Iversen, Luke Thomas, Dennis Praet, Wilfred Ndidi, Ayoze Pérez and Vardy – playing his 400th game for the Club – also came into the XI.
With only 28 seconds on the clock, Justin's half-volley deflected wide off the body of Pérez after the full-back was urged to shoot by the Blue Army. In torrential rain, Harvey Barnes, having scored at Everton over the weekend, had a strike turned to safety by a glut of Newport defenders.
Only some last-ditch defending from Adam Lewis prevented Vardy, who had latched onto Barnes' through-ball, from locating the run of Pérez, denying the Spaniard a certain goal on eight minutes. The momentum was with the home side, with Pérez again threatening after cutting inside and drilling over with his left boot.
Justin continued to create from the right, dropping a ball into Vardy, who flicked down into the path of Praet. The No.26, who was absent from the squad to face Everton after the birth of his child, took a touch and fired wide. Midfielder Boubakary Soumaré followed up with a wayward attempt not long after.
A brilliant one-two between Barnes and Vardy mustered up the next opportunity, with the former testing Nick Townsend with a placed attempt that the 'keeper was equal to. City were still dominating, and it was only a matter of time before the opener would arrive.
With only a minute of the first 45 to go, Justin cut in from the right wing, playing a give-and-go with Praet, and bent a beautiful left-footed shot into the inside of the post from 20 yards, scoring for the first time since February 2021. The Foxes were deservedly in front at the interval.
A combination of Wout Faes and Iversen – the latter making his home debut for the Foxes – successfully cleared James Waite's dangerous cross from the right flank as Leicester had to defend their goal. Shortly after, Mickey Demetriou struck the post with a header, however the fourth official's flag would later go up for offside.
Iversen was called into action again just before the hour mark, with Adam Lewis this time heading straight at the Dane. Moments later, a pause in play came as Justin required treatment on the pitch, with the full-back taken off on a stretcher. On came vice-captain Marc Albrighton, while Youri Tielemans and Kelechi Iheanacho both came on with Soumaré and Pérez making way.
Townsend had to smother Vardy's shot on 65 minutes, with substitute Iheanacho making an immediate mark on the match by playing the No.9 through. A lovely turn and run from Academy graduate Barnes two minutes later forced another good stop out of the Newport shot-stopper, who was keeping his side in the match.
He could do nothing about City's next attempt on 70 minutes. Iheanacho stretched the play and found Albrighton wide right. The No.11 whipped a pin-point cross into Vardy, whose flicked header squirted past Townsend for 2-0. On his 400th appearance, he netted his 166th goal across all competitions, bowing to the Newport supporters after receiving some flack earlier in the encounter.
Another Leicester milestone followed, with Academy star Sammy Braybrooke coming off the bench to make his professional debut for his boyhood football club, having spent over a decade of progression through the ranks with the Foxes. Nigeria international midfielder Ndidi made way.
Into the final 15 minutes, Jannik Vestergaard was introduced in place of Faes, and as Newport looked to halve the deficit, the Foxes struck again. Vardy was played through by Barnes and the striker rounded Townsend and cut past Priestley Farquharson before smashing in for Leicester's third.
There was still time for Iversen to match substitute Thierry Nevers' low attempt from distance, while Townsend made a similar save late as he held onto Iheanacho's first-time strike. In time added on, Vestergaard flicked a header goal-bound, but Townsend was there again, bringing to a close the third round tie.
Major moment – Justin curls in
The Welsh outfit had remained compact throughout large parts of the first half, however when James Justin burst into space on the edge of the box, Nick Townsend could do nothing about his strike as he curled in from distance in brilliant fashion.
Who impressed – Vintage Vardy
Legend Gerry Taggart told LCFC Radio at full-time: "With two goals tonight, it’s got to be Jamie Vardy who gets my Man of the Match. He could have had a hat-trick, too."
Where do we stand – Into round four
City will discover their fourth round opponents on Thursday night, with the tie taking place in the week commencing 19 December, 2022.
Coming up – West Ham (A)
The Foxes will take on West Ham United at London Stadium in the Premier League on Saturday (3pm GMT kick-off), their final fixture before the winter break.