Humble Welsh club Newport had led from the 10th minute but their dream appeared to have been snatched away when Rachid Ghezzal smashed in a late equaliser, only for Padraig Amond to send the Rodney Parade faithful insane with a penalty victor.
Newport County striker Padraig Amond celebrates after scoring their 2nd goal from the penalty spot during the FA Cup match against Leicester City at Rodney Parade in Newport. Elsewhere, QPR ended a 22-year wait to win an FA Cup tie at the first time of asking as they beat Championship leaders Leeds United, while Sheffield United went down at home to National League side Barnet.
Premier League champions Manchester City and Watford had no such problems, claiming 7-0 and 2-0 wins over Rotherham and Woking respectively.
Newport's only previous FA Cup meeting with Leicester was their first-ever match in the competition proper - they lost 0-2 in a replay in the 1919-20 campaign.
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Claudio Ranieri's Fulham reign has got off to a hard start and it got worse for the former Leicester boss at the hands of Pete Wild's Oldham.
Callum Lang then sent 4,000 travelling Oldham fans wild with a headed victor in the 88th minute.
"I think we need to be ready because I know the tradition of the cup", he told a press conference.
The other big upset of the day occurred when non-league Barnet beat Sheffield United 1-0. "It's one of those where you don't want them having any experience of lower-end stuff because hopefully it will catch them out".
Pep Guardiola's Manchester City joined Manchester United, Tottenham, Chelsea and Arsenal in the fourth round with a romp.
It turned into a rout after the interval, Gabriel Jesus netting from Sterling's precise cross, with Ilkay Gundogan then turning provider for City's final three goals - Riyad Mahrez, Nicolas Otamendi and Leroy Sane getting in on the act.