The vast majority of the damage was dealt in the first leg when Man City ran riot in a 9-0 demolition, but League One Burton salvaged pride from the home leg as they limited the holders and English champions to only a 1-0 win at the Pirelli Stadium.
Sergio Aguero scored the only goal of the night as Man City edged past their spirited hosts, setting up a Wembley final against either Tottenham Hotspur or Chelsea on February 24 when Pep Guardiola's side will attempt to retain the trophy.
It took only nine minutes for Man City to break the deadlock in the reverse fixture, but Burton offered early signs that they were not only there to make up the numbers and held their own during the opening exchanges against a team including the likes of Aguero, Kevin De Bruyne and Riyad Mahrez.
City chances were inevitable, though, and Mahrez missed the target twice when he might have done better in the opening quarter of the game, first firing wide from a tight angle before curling a trademark finish just past the far post from the edge of the area.
Burton threatened an opener of their own after 14 minutes when Fabian Delph's complacent play earned the hosts a free kick which Stephen Quinn fired low into the area and Liam Boyce cleverly flicked goalwards to force a save from Arijanet Muric.
City's star trio were all involved when the goal did come, with De Bruyne releasing Mahrez, who in turn dropped the ball back for Aguero to sweep a routine finish past the keeper and bring up double figures on aggregate.
It was a goal around the half-hour mark which opened the floodgates at the Etihad Stadium, but there was no repeat this time around and Burton responded quickly with Will Miller firing wide from range and Muric almost letting the ball trickle over his own line when under pressure.
Burton were hit by the blow of losing Ben Turner to injury before half time, but they prevented City from building on their advantage before half time, with a half-chance for Eric Garcia from De Bruyne's free kick the closest the holders came to a second.
Nigel Clough made his second change during the interval with Ben Fox replacing Quinn and the home side once again looked to start quickly as David Templeton turned smartly in midfield before firing a long-range effort well over.
The second half soon fell into a familiar rhythm, though, as City dominated possession without playing anywhere close to their usual intensity having already wrapped up their place in the final earlier this month.
Delph should have doubled their advantage when he darted into the box to meet a Danilo cross, but he missed the ball with his first effort before being denied by Bradley Collins when a lucky bounce afforded him a second bite at the cherry.
Aguero uncharacteristically missed a golden opportunity to double his personal tally shortly after the hour mark when he put wide with the goal gaping, although VAR would have ruled it out for offside against Phil Foden in the buildup.
Guardiola welcomed Benjamin Mendy back from injury as a 63rd-minute sub before Danilo was then caught in two minds to waste another good position, and the Premier League champions should have been punished for their lethargy with 20 minutes remaining when Burton created their clearest chance of the entire tie.
A slip from Philippe Sandler was quickly pounced upon and, while Boyce's poor touch caused his own chance to go begging, the ball bounced back out to Miller, who was only denied by a last-ditch Garcia block on the line.
It proved to be their best chance to nick a goal - or even a draw - against the champions of England, but Burton did at least avoid the ignominy of equalling the heaviest ever League Cup aggregate defeat of 11 goals as Collins made late saves to deny Gabriel Jesus and Danilo.
Man City will now wait until tomorrow night to find out the identity of their opponents in next month's final, with Tottenham currently holding a 1-0 advantage over Chelsea ahead of the second leg at Stamford Bridge.
BURTON (4-2-3-1): Collins; Akins, McFadzean, Turner (Hutchinson 40'), McCrory; Quinn (Fox 46'), Wallace; Harness, Miller, Templeton; Boyce (Daniel 77')
MAN CITY (4-3-3): Muric; Danilo, Sandler, Garcia, Zinchenko (Nmecha 67'); Foden, De Bruyne (Mendy 63'), Delph; Mahrez, Aguero (Jesus 63'), Poveda
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