Kevin de Bruyne, Oleksandr Zinchenko, Phil Foden, Kyle Walker and Riyad Mahrez were also on target against Nigel Clough's League One side as City ensured their visit to the Pirelli Stadium on January 23 is a mere formality.
"Of course we are already in the final. We have to play second leg and we will take it seriously. Happy to be in the final again," said City boss Pep Guardiola. "It's not easy to play this kind of game. We spoke (before the game) to take it seriously, we started well."
After also thrashing Rotherham 7-0 in the FA Cup on Sunday with a much-changed side, Guardiola was able to again hand a rest to a number of his key players but named a strong side with De Bruyne continuing his comeback from injury.
And the Belgian set the tone for the evening by heading City into a fifth-minute lead as he timed his run into the box perfectly to head home David Silva's cross.
Clough admitted before the game it would take a "miracle" for Burton to blunt the Premier League champions' might over two legs.
"We didn't expect anything less given the gulf in class between the teams, we actually feared it could be more," said Clough, a two-time League Cup winner as a player under his father Brian Clough at Nottingham Forest. "We've made history with the club getting to the last four of a Cup competition. Once we saw the three teams (in the semi-finals) it was always going to be trouble."
So it proved, but the visitors missed a glorious chance to get straight back on level terms when Marcus Harness blasted over Lucas Akins's cross when completely unmarked inside the penalty box.
It took City until the half hour mark to double their advantage, but a glut of three goals in seven minutes followed to put the tie to bed before the break.
Jesus headed home his first from close range after Bradley Collins had denied Leroy Sane before the Brazilian slotted home Silva's cushioned pass via the inside of the post.
"Players like me want to play more, to help the team, and we went out there to win," said Jesus.
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