Kevin De Bruyne, Oleksandr Zinchenko, Phil Foden, Kyle Walker and Riyad Mahrez also scored at Etihad Stadium for a result that virtually renders the second leg meaningless in two weeks.
Zinchenko's strike was his first for City, though whether or not he actually meant it is a matter of debate - the 22-year-old Ukrainian flooping a lofty cross-cum-shot Burton 'keeper Bradley Collins from the edge of the area.
"We do what we have to do to become a great, great club", warned Guardiola.
It's not unthinkable that City could win an unprecedented quadruple this season and continue their domination of the English game, whilst Burton look to have a task on them to even make the League One playoffs.
Looking Ahead It would take somewhat of a miracle for City to not progress and we can assume that they are guaranteed another League Cup final under Pep Guardiola.
We've not gone into any detail with them (the players) because that will frighten the life out of them.
Of course, City added five more goals in the second half.
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"We've not gone into any detail with them because that will frighten the life out of them", admitted Clough.
"Manchester City are the current Premier League champions, it is over two legs so we will go there on Wednesday and we will enjoy the occasion but I think it is about damage limitation after seeing the demolition of Rotherham in the FA Cup on Sunday". Nobody gives us much of a chance and rightly so but it's just about the players, everybody, talking about supporters, who have been following the club for 50-60 years never dreamt of us being in a League Cup semi-final.
"We made good runs in behind and we took it seriously".
The Gunners managed to qualify to the fourth round after they convincingly beat Blackpool over the weekend where Elneny was given his regular start by Unai Emery in cup competitions.
"Players like me want to play more, to help the team, and we went out there to win", said Jesus.
Jesus continued his troubling act on the hapless visitors by completing his hat-trick with a flawless header from close range on 57 minutes. "When you get to the semi-finals and you have beaten Premier League teams and mythic teams like Aston Villa or Middlesbrough, the reason why they are here, they deserve incredible credit".