The Foxes battled gamely, levelling an early opener from Carlos Tevez through Paul Gallagher's penalty, but two goals in 77 seconds from Patrick Vieira and Adam Johnson gave the hosts a 3-1 lead at the break.
Tevez then saw his penalty saved by Chris Weale before Lloyd Dyer reduced the deficit further with seven minutes remaining. City, however, put the tie beyond their Championship opponents when Aleksandar Kolarov lashed home a fourth in the final minute.
It was a fitting tribute to Neil Young - the terminally ill member of the side that triumphed at Wembley in 1969, for whom the City players posed for the pre-match photograph wearing distinctive red and black striped kits.
City's latest attempt to emulate that team got off to a stuttering start 10 days ago and for half an hour they were no more convincing at the second attempt, despite boasting the most expensive starting line-up in FA Cup history.
The £162million included hefty fees for Yaya Toure, David Silva and Tevez, who remains Roberto Mancini's talisman for all the other additions.
It was hardly a surprise that Tevez should put City ahead.
Turning sharply past Yuki Abe as he collected a throw from fellow Argentinian Pablo Zabaleta, Tevez then ran straight at Jack Hobbs.
A fortunate bounce off the former Liverpool man allowed Tevez to continue his charge towards the box and, with one swipe of the right boot, he lashed a shot into the corner.
City were not in front for long though as Lloyd Dyer burst between Joleon Lescott and Vieira, falling over the latter man's leg, which had been conveniently dangled out.
Gallagher's approach was unconventional, keeping his back to goal for as long as possible. His finish was effective though as Joe Hart went the wrong way.
For a while, City wobbled and Eriksson could dream of causing a cup shock against the club he left so abruptly, dumped by discredited former owner Thaksin Shinawatra in May 2008.
But this Blues outfit are not as fallible as Eriksson's were - nor any other City manager's in recent memory.
And in the space of 77 seconds towards the end of the opening period, the Premier League title chasers took control.
This time, Tevez was the creator, lifting a superb pass beyond the Leicester defence to Zabaleta.
Silva met the South American's cut-back and, though Souleymane Bamba blocked on the line, the ball screwed across the six-yard box to Vieira, who tapped into an empty net.
Then Silva spotted Johnson's defence-splitting run and slipped a precise pass to the England midfielder that left him with only Chris Weale to beat.
Having blown one such opportunity when the tie was still goalless, Johnson was in no mood to let Leicester escape a second time and finished with clinical efficiency.
Unsurprisingly, City adopted a more conservative approach to their attacking after the break, content to use the pace of Johnson and Tevez to keep the Leicester defence on their toes.
Any lingering hopes for the visitors should have been snuffed out when Tevez went down as he cut inside Hobbs.
As the defender was the last man, it warranted a red card. Mancini certainly thought so, waving his arm to that effect.
But referee Mark Halsey decided otherwise - a decision that became more significant when Tevez blasted the spot-kick straight at Weale's legs.
Mancini was presumably thinking about it even more when an accidental intervention from the referee offered Abi a second opportunity to play a pass beyond the City defence, which Dyer profited from after shrugging off Vincent Kompany.
The Blues boss must be heartily sick of such endings, having endured a similar situation against Wolves on Saturday.
But Kolarov strode forward to end any doubt and set up a visit to Paul Ince's League One outfit, who dumped Sunderland out 10 days ago.