It was an afternoon that saw Eriksson pit his wits against a former apprentice in current Manchester City boss Robert Mancini, who played under Eriksson for eight years at Sampdoria and Lazio.
Mancini's first coaching role was also under Eriksson at Lazio, and his old boss's current side can consider themselves slightly unfortunate not to have claimed a famous FA Cup scalp.
The match got off to a blistering start when Bamba, making his debut after joining from Hibernian, gave the hosts a dream start with his first touch in English football.
Paul Gallagher was a constant menace with his superb deliveries all afternoon, and his cross from the left was flicked by Jack Hobbs into the path of the unmarked Bamba, who bundled the ball home.
It was the first of a series of chances for the French central defender, who used his physical presence to ruffle the opposition at set pieces.
He forced a brilliant reaction save from Hart with a bullet header later in the first half, while Japan international Yuki Abe forced an athletic stop from the City keeper with a 25-yard drive after jinking past Milner.
It took Mancini's side some time to come to terms with Leicester's fast start, but they should have levelled through Patrick Vieira, who was one of six changes from the City side that drew 0-0 at Arsenal on Wednesday.
The midfielder was unmarked six yards from goal but made poor contact with his volley and Chris Weale saved.
Milner's equaliser was pure class, with the midfielder collecting a return pass from Tevez before ghosting beyond Bamba and shooting past Weale.
His goal came just shy of 24 minutes - the point at which the visiting fans turned away from the action for a minute in honour of Neil Young, the Manchester City great who has been diagnosed with terminal cancer.
It was after 24 minutes of the 1969 FA Cup final against the Foxes that Young struck the only goal of the contest, and supporters also wore red and black scarves, replicating their team's colours that day.
In contrast, Adam Johnson wasted a great chance for the Premier League side before the break, failing to convert Milner's low pass across goal from six yards with the unmarked Jo in a slightly better position just behind him.
But Tevez did ensure City went in ahead, slotting home with the inside of his right heel at the near post from Milner's low cross.
Mancini tweaked his team's formation after the interval, with Nigel de Jong replacing the largely ineffective Shaun Wright-Phillips as City switched from 4-4-2 to their usual 4-3-3.
The Foxes should have equalised through Hobbs, who was left completely unmarked at the far post from a Gallagher corner, but headed wastefully wide.
Leicester continued to play at a high tempo and eventually equalised, thanks in part to poor goalkeeping from England's Hart.
Gallagher's cross from the left bounced awkwardly in front of Hart, who should still have gathered the ball but spilled it into the path of King, who slotted home.
Leicester really took the game to their opponents after King's goal, and it took a goal-line clearance from Milner to prevent Bamba from heading the Foxes back in front after Mancini's side yet again failed to deal with a set piece.
The visiting side did create one clear opening when the largely anonymous Tevez swivelled and played in an unmarked De Jong, but Weale saved his shot.
Tevez himself had a shot from a tight angle saved in the dying minutes, but a late winner for the visitors would have been very tough on the Foxes.
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