The Premier League champion has now put 16 goals past lower-league opposition in the past four days, Pep Guardiola's men having thrashed Rotherham United 7-0 in the FA Cup at the weekend.
Kevin De Bruyne's first headed goal in English football set the hosts on their way, with Jesus adding a quick-fire double before Oleksandr Zinchenko fortuitously opened his City account.
Jesus took his tally to four either side of Phil Foden's tap-in, before Kyle Walker and Riyad Mahrez completed a miserable night for Burton's cup heroes.
It took City five minutes to unlock the Burton defence, David Silva's pinpoint pass picking out De Bruyne's run and the Belgium international made no mistake with his header.
Despite falling behind Burton rallied and Marcus Harness should have equalised in the 12th minute, but the weekend's hat-trick hero blazed Lucas Akins's cross over the bar.
City's control of proceedings was never under threat, though, and in the space of seven minutes the hosts were four goals ahead as Jesus and Zinchenko struck.
Having pounced on a loose ball after Leroy Sane's shot was saved by Bradley Collins, Jesus doubled his tally from Silva's pass, the striker taking his time before slotting it in off the post.
City's fourth was harsh on the visitors as Zinchenko's attempted cross looped over Collins, but there was no doubting the quality of Jesus's hat-trick goal as he converted Mahrez's cross to the back post.
Four minutes after replacing the impressive De Bruyne, Foden had his second goal at Etihad Stadium in as many games, the youngster profiting after Jesus had been held up by Burton's defenders.
Jesus would not be denied a fourth moments later, however, as Sane beautifully controlled Mahrez's pass on his chest before finding the striker, who applied the finishing touch.
After setting up Walker for City's eighth, Mahrez completed Burton's misery with a goal of his own, the Algeria international poking the ball past Collins to round out a one-sided semi-final encounter.