The Nigeria striker found the net after just four minutes at Griffin Park, after an exquisite Dennis Praet pass found James Justin, who crossed for Iheanacho to convert from close range.
Manager Brendan Rodgers made nine changes from the starting line-up which overcame West Ham United on Wednesday, with Ayoze Pérez and Çağlar Söyüncü keeping their places.
City could have taken the lead inside just 15 seconds as Demarai Gray won possession before the deflection fortuitously landed to Iheanacho, who subsequently slid it in for Pérez.
However, just as the Spaniard set his sights on goal, in came Luka Racic for the Bees to block his powerful effort, although the Foxes were minutes away from going ahead.
It came as Praet collected the ball on the half-way line, fizzing an excellent pass through Brentford’s defensive lines, locating Justin on the right flank with remarkable precision.
Justin swiftly crossed for Iheanacho in the middle and, in the end, it was a simple finish for the 23-year-old, who also provided two assists in Wednesday’s 4-1 triumph over West Ham.
On 14 minutes, another smart effort from Iheanacho, on the edge of the area, was kept out by Bees shot-stopper Luke Daniels, while Marc Albrighton fired wide on the half-hour.
At the other end, Danny Ward was called upon to get a hand on Dominic Thompson’s low curler, tipping it round the post, but most of the action took place in the home side’s penalty area.
Pérez saw another attempt saved by Daniels minutes before the interval, while Albrighton headed over shortly after, but the second period was a more relaxed affair for the Foxes.
Perhaps the biggest moment for Thomas Frank’s Sky Bet Championship side came in the 64th minute when Emiliano Marcondes clipped the post, prompting Christian Fuchs to scramble it away.
With 22 minutes to play, the next Academy star to step up into the first team came in the shape of Kiernan Dewsbury-Hall, who has impressed for the Development Squad this term.
The central midfielder came on for goalscorer Iheanacho and will be pleased with his contribution for Rodgers’ seniors, who were able to hold out for a clean sheet.
However, they needed a fine, quick-thinking save from Ward to achieve that feat, with the Wales international managing to stop Racic’s first-time shot from levelling it on 83 minutes.
The home side also had a goal disallowed in the latter moments, but the Foxes were good value for their win – a second success in a week ahead of another crucial period in their season.
Major moment
City got off to a flier at Griffin Park with Dennis Praet and James Justin linking up wonderfully before the latter laid it up for Kelechi Iheanacho to net for the visitors.
While Leicester will have been frustrated not to add more, the defensive players were able to keep Brentford out for the next 86 minutes, putting the Foxes in the hat for the fifth round.
Who impressed?
Speaking on LCFC Radio, former Leicester City captain, Matt Elliott, said: “The back four were in reasonable control for the majority of the time. Christian Fuchs got the TV Man of the Match award, but I’m going to give it to Wes Morgan. Well played, sir!”
Where does it leave us?
Leicester head into the fifth round of the Emirates FA Cup, which is scheduled to take place between Tuesday 3 March and Thursday 5 March.
The draw, on the other hand, will be staged at 7:19pm on Monday 27 January, before AFC Bournemouth's fourth round tie against Arsenal at Vitality Stadium, and Leicester will be ball no.7.
Coming up…
A Carabao Cup Semi-Final second leg tie stands between City and a first cup final since 2000 at Aston Villa on Tuesday evening (7:45pm kick-off), before Chelsea visit King Power Stadium in the Premier League on Saturday (12:30pm kick-off).
All times GMT.