New-boy Fousseni Diabate burst onto the first-team stage with two goals and a man-of-the-match display on his debut.
And boss Puel then revealed how son Gregoire gave him in the inside track on the Malian forward, who signed this month for £2m from Corsican club Gazelec Ajaccio.
Gregoire was a Gazelec team-mate of Diabate in the French Second Division - the same division where the Foxes discovered Premier League title-winning star Mahrez four years ago.
“I used my own opinion but my son knows Fouss very well and he gave me good news about him and about his positive, professional attitude,” said Puel senior.
“He said he was a good man and a good player and it was important for him to show this in his first game.
“My son played with him and I followed his games and I thought this player could have good attributes to play in the Premier League in the future.
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“I used my own opinion but my son knows Fouss very well and he gave me good news about him and about his positive, professional attitude”
Leicester boss Claude Puel
“In France a lot of clubs knew this player and at Ajaccio he was a good player but without perhaps being clinical and without a fantastic game.
“But it was important to feel something about him and good attributes for the future and with good work.
“Of course he is not the same quality and the same possibility at the moment as an experienced player like Mahrez but I think for the future he will be a good solution.
“It’s important to look not just at the great teams, but to look for young players with quality and then try to develop them.”
Diabate announced his arrival just nine minutes into his debut, collecting a smart pass from Adrien Silva and producing a fantastic finish to open the scoring.
Kelechi Iheanacho doubled the lead three minutes later when he found the bottom corner from 20 yards and the £25m summer signing volleyed home a Christian Fuchs cross to make it 3-0 on 29 minutes.
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Andrew Hughes forced in a shot on the turn for Posh three minutes into the second half to give them hope.
But Diabate matched Iheanacho’s brace with three minutes left when he buried a rebound after goalkeeper Jonathan Bond saved from Demarai Gray.
Wilfred Ndidi completed the scoring with the final kick of the game, finishing from 12 yards after another fine run by Diabate.
The Foxes have not won the FA Cup in their 134-year history and Leicester-born midfielder Harvey Barnes said: “You just have to take every round as it comes and every round is a step closer.
“It would be great if we could progress closer to the final.”
Posh will return to League One duty, where they are four points outside the play-offs and defender Liam Shephard said: “Promotion has been the main focus from the start of the season.
“We know we are capable of being in the Championship.”
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PETERBOROUGH (4-2-3-1): Bond 6; Shephard 6, Taylor 5, Tafazolli 5, Hughes 6; Forrester 5, GRANT 7; Maddison 6 (Borg 89), Lopes 5 (Morias 61, 6), Lloyd 5 (Kanu 79); Marriott 6. Subs: O’Malley, Baldwin, Penny, Doughty.
UP NEXT: Southend (h), League One, Saturday.
LEICESTER (4-2-3-1): Hamer 6; Simpson 6, Benalouane 6, Maguire 7, Fuchs 7; Iborra 7 (Albrighton 64, 6), Silva 7; DIABATE 9, Barnes 6 (Ndidi 64, 7), Gray 6; Iheanacho 8 (Chilwell 79). Subs: Jakupovic, Huth, Vardy, Mahrez.
UP NEXT: Everton (a), Premier League, Wednesday.
Referee: Michael Oliver 7
Your turn: What was the score when Peterborough last hosted Leicester, in the Championship in February 2013?
Star player: FOUSSENI DIABATE - Dream debut
Star shocker: LEO DA SILVA LOPES - Nothing went right
Match rating: 3