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.
After being criticised for fielding a weakened side in the Foxes' Carabao Cup quarter-final defeat to Manchester City last month, Puel's much-changed line-up on Sunday drew added scrutiny.
Daniel Iversen compounded Fulham's misery by saving an Aleksandar Mitrovic penalty - his first touch after coming off the bench - just moments earlier.
The FA Cup is back, and the famous old magic is still well and truly alive thanks to some incredible third-round matches.
National League Barnet were the big winners as Shaq Coulthirst's first half penalty led the 14/1 (15.0) Bees past Sheffield United of the Championship on Sunday afternoon.
"It´s unbelievable - that´s the only word I have at the minute", said Barnet captain Callum Reynolds after the north London club´s triumph.
'We had loads of half-chances, some very good positions where we should score, and on another day they all go in.
"I think we lost together, we are all together disappointed and frustrated after this game, because it was an objective for us".
It was the same result as Manchester United beat Reading to make it five wins out of five under caretaker boss Ole Gunnar Solskjaer.
Saturday also saw Championship club Bristol City beat top-flight basement club Huddersfield 1-0.
Elsewhere, League One Doncaster enjoyed a superb 3-1 away win at Championship side Preston.
Premier League strugglers Fulham were up-ended by League Two Oldham.
Manchester City, meanwhile, thrashed Rotherham 7-0 at the Etihad as Pep Guardiola named a strong side following the win over Liverpool on Thursday.
11th-hour deal allows Sears to remain open - for now
The creditors' attorneys question whether the terms of those loans unduly benefited Lampert and his hedge fund rather than Sears. It is known he expects the new Sears to borrow $1.3 billion from three leading banks.