Kevin De Bruyne's first headed goal in English football set the hosts on their way, with Jesus adding a quickfire double before Oleksandr Zinchenko fortuitously opened his City account.
After setting up Walker for City's eighth, Mahrez completed Burton's misery with a goal of his own, the Algeria global poking the ball past Collins to round out a one-sided semi-final encounter.
He said: 'It's the first time I've played in a win like this.
Gabriel Jesus struck four times for City and said afterwards that he was satisfied with the way Pep Guardiola's side didn't let up.
"We didn't play brilliantly and a couple of the goals we were disappointed with, as we should have defended them better, but the gulf in quality was very evident and the players came in at half-time and were wide eyed with what they have played against. In this incredible schedule, we have a little bit of a break in that week to prepare for the other competitions".
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As is common in the competition, Guardiola has used the League Cup to give his full squad a run-out.
Sane was nearly through at the start of the second half only for his touch to let him down, but Burton showed they had not given up as Scott Fraser shot over following more good work from Akins. "If you are 4-0 up and forget to continue, you don't have respect for the competition or your opponent".
The two teams meet at the Etihad for the first leg as they battle to face Tottenham or Chelsea in the final at Wembley. "The best way is do what we have to do". They beat mythical teams - like Aston Villa and Middlesbrough. Not at all, we have made history in getting this far.
The second leg, merely a formality, takes place on Wednesday, 23 January.
"The only way is to take it seriously".
All we'll say is that he looked mighty bashful while celebrating... "That's what we have done and that's why we are pleased".