League One Burton, managed by Nigel Clough, the son of former Nottingham Forest boss Brian, must endure another 90 minutes at their own ground on Jan. 23 before City formally book their place in the final.
Hundreds of Burton fans arrived late after their buses were stuck in motorway delays and after this mauling, they might well wish they had turned around and gone home.
City, who beat Championship (second tier) side Rotherham United 7-0 on Sunday, are set to face the winners of the other semi-final between Chelsea and Tottenham Hotspur, which Spurs lead 1-0 from the first-leg.
Manager Pep Guardiola fielded a strong starting line-up and City quickly established their dominance with Kevin De Bruyne steering in a header from an excellent lofted ball from David Silva to open the scoring in the fifth minute.
Burton should have drawn level in the 12th minute but Marcus Myers-Harness wasted a glorious chance, shooting wastefully wide when left unmarked at the back post.
From then on it was a painful night of damage limitation for the team from the Midlands.
Jesus opened his account on the half hour, heading in from close range after Leroy Sane’s shot had been blocked by keeper Bradley Collins, with the ball popping up invitingly for the Brazilian.
Four minutes later, Jesus made it 3-0 with a low drive that went in off the post and then Ukrainian Oleksandr Zinchenko added the fourth, lobbing Collins with a lofted shot from nearly 30 metres out.
Jesus completed his hat-trick in the 57th minute with a header from a Riyad Mahrez cross before substitute Phil Foden made it 6-0 in the 62nd -- slotting home after Collins had blocked a Jesus shot.
The seventh -- and Jesus's fourth -- was a clever flick from close-range after Sane had once again burst into the area on the left flank.
Burton were completely unable to defend that part of the field and even with Sane subbed off, Mahrez broke into that area and his low cross was turned in by Kyle Walker to make it 8-0.
Mahrez poked in the ninth after good work from substitute Bernardo Silva and that was all for City despite the crowd urging them to push for a 10th goal.
City's record victory was a 12–0 FA Cup win over Liverpool Stanley in 1890. The Blues beat Huddersfield Town 10-1 in the old Division Two in 1987.
(Reporting by Simon Evans; Editing by Toby Davis)
