The tie was already over after City’s remarkable 9-0 first-leg win but Pep Guardiola still named several first-team stars in a weakened line-up.
Sergio Aguero scored the only goal of the night from Riyad Mahrez’s pass after good play from Kevin de Bruyne.
Burton did have chances with Will Miller’s shot cleared off the line.
EFL Cup holders City will face either Chelsea or Tottenham in the Wembley final on Sunday, 24 February.
Spurs lead 1-0 going into Thursday’s semi-final second leg against the Blues at Stamford Bridge.
Aguero continues EFL Cup form in strange game
City’s sensational win in the first game made the second leg, played in the freezing cold, a formality. It was arguably the lowest-key semi-final the competition has seen.
Guardiola named City’s youngest XI in over a decade, with eight changes from the weekend’s Premier League win over Huddersfield.
But the three regulars in the line-up combined for the goal. De Bruyne was playing in a deep midfield role as he builds his fitness following an injury. He played a long ball out to the right for £60m winger Mahrez, who found Aguero – with City’s all-time top scorer sweeping home in the box.
Aguero, who missed a simple chance to make it 2-0 in the second half, has scored in five of his past six League Cup semi-final appearances.
City handed a debut to England Under-19 winger Ian Carlo Poveda, who was lively, and Eric Garcia blocked a shot on the line after fellow young defender Philippe Sandler lost possession.
Goalkeeper Arijanet Muric looked shaky on more than one occasion but kept his fourth clean sheet in five EFL Cup games this season.
Guardiola made substitutions in the second half – with France left-back Benjamin Mendy returning from injury and 18-year-old Felix Nmecha coming on for a debut.
There was never any danger of a Burton comeback and City are 90 minutes away from retaining the trophy next month.
Burton have their day – but not their goal
Burton’s finest hour, in reaching their first-ever major national semi-final, will be forever remembered for the first-leg demolition.
But they restored some pride, even if they could not score the goal which boss Nigel Clough had longed to see.
In front of a partisan crowd of 6,519, they created chances with Liam Boyce forcing a save with a back-heel and David Templeton shooting over from long range early in the second half.
Templeton also had a penalty appeal turned down when he was tackled by Danilo on the edge of the box.
A huge roar from Burton’s crowd met their best chance as Miller’s shot was cleared off the line by Garcia after Muric had saved a Boyce effort.
Now their attentions must turn back to League One, with the Brewers only six points above the relegation zone.
‘We got our pride back’ – manager reaction
Burton manager Nigel Clough: “We were close two or three times but I’m very pleased with how we played.
“We got our pride back. We did everything we could. Being at home, the pressure was off as the tie was over but we put in a good performance against top players.
“We were brave on the ball, played it when we could and we caused them problems. I watched the last few Premier League games and we caused them as many problems as Wolves and Huddersfield did.
“The youngsters will learn so much from being on the same pitch as these magnificent players. Hopefully we have made a few quid from the run but it’s more about the experience.”
Manchester City boss Pep Guardiola: “It went well. The pitch was so dangerous and slippery, but we had a good game. We missed the last pass and the finishing a little bit, but it was good.
“The game was completely different from the first leg because we started with a 9-0 lead, but I didn’t see a lack of desire or playing like we believed we were something we are not.
“We will try to win this competition, but the important thing is being there for a second year in succession. We take the Carabao Cup seriously and have done in all the games we played. We are in another final and now we’re going to try to prepare well to try to win.”
Man of the match – Eric Garcia (Man City)
City break their own record – match stats
Manchester City have reached consecutive League Cup finals for the first time. Manchester United were the last team to both reach and win consecutive finals in the competition in 2008-09 and 2009-10.
It is the biggest semi-final aggregate win in League Cup history – overtaking their 9-0 aggregate win against West Ham in 2014.
Since Liverpool’s Roberto Firmino scored against them on 3 January, City have gone 476 minutes without conceding, while claiming 24 in reply.
City have conceded just one goal in the League Cup so far – Leicester’s Marc Albrighton scoring an equaliser in the quarter-finals.
City have kept five successive clean sheets for just the second time under Pep Guardiola – also doing so November 2018.
Mahrez was directly involved in four of Man City’s 10 goals against Burton – one goal and two assists in the first leg and an assist in the second leg.
Burton, who are 13th in League One but not safe from relegation, host struggling Bradford on Saturday (15:00 GMT). City host Burnley in the FA Cup fourth round at the same time.