The Premier League outfit went into this evening's second leg trailing their Championship opponents 1-0 after Boro's surprise win at the Riverside Stadium earlier this month.
However, that deficit was wiped out within 15 minutes courtesy of a Jonny Howson own goal, and Chelsea had effectively sealed their passage to Wembley before half time at Stamford Bridge.
Further goals from Enzo Fernandez, Axel Disasi and Cole Palmer saw Mauricio Pochettino's men race into a 4-0 lead on the night before the interval, and Palmer and Noni Madueke added another two quickfire strikes late in the second half.
Boro pulled one back with a couple of minutes of normal time remaining as Morgan Rogers curled in a consolation, but Michael Carrick's men were well beaten as they saw their dreams of reaching Wembley ruthlessly swept aside.
The Championship club largely had themselves to blame though, with four of the goals coming as a result of them losing possession when trying to play out from the back, in addition to the own goal which opened the scoring.
The 6-1 scoreline on the night equals the biggest-ever EFL Cup semi-final second leg victory, while Chelsea are also only the second team to score six goals in the second leg of a semi-final in the competition.
Pochettino's hopes of landing a trophy in an otherwise difficult first season as manager looked under serious threat following the first leg, during which they notably wasted three big chances, but Chelsea were prolific rather than profligate this time around and quickly atoned for their performance at the Riverside.
The opening goal of the night may have come from a red shirt, but it was slick Chelsea play that led to it, with the fit-again Ben Chilwell's through-ball finding Raheem Sterling, who unselfishly squared it to Armando Broja.
The striker, who has been linked with a move away from the club this month, failed to bring the ball under his control immediately, but in his haste to get back Howson only succeeded in diverting it into an empty net.
Rogers had a sight of goal at the other end shortly afterwards which could have seen Boro regain the aggregate lead, but he put his shot too close to Djordje Petrovic.
Twelve minutes later, it was Chelsea that took the lead in the tie, and again it came at the end of an incisive team move that saw Sterling back-heel the ball to Disasi, who cut it back into the middle.
Once again, Broja failed to take full advantage as he miscued his attempted finish, but the ball still ran through to Fernandez, who applied a much more accomplished finish.
Chelsea did not look like they needed a helping hand, but each of their next four goals all stemmed from Middlesbrough mistakes as they tried to play out from the back.
The hosts' third came as Disasi nicked the ball on the halfway line and continued his charge forward to get on the end of Sterling's low cross, guiding a first-time finish past the keeper.
Boro then gave possession away again on the edge of their own box just five minutes later, this time Palmer picking their pockets and stroking the ball into the bottom corner to make it 4-0 on the night before half time.
It was a similar story once more for Palmer's second of the night, with Conor Gallagher winning possession inside the opposition half before making his way to the byline and cutting the ball back for his compatriot to apply the clinical finish.
The sixth of the night followed just four minutes later, with Gallagher again the creator as he pounced on yet more loose play from Middlesbrough in their own half before finding Noni Madueke, who cut inside before firing home, despite the best efforts of Rav van den Berg on the line.
Boro had the ball in the back of the net at the other end of the pitch one minute later as Matt Crooks glanced a header into the far corner, only to see his celebrations cut short by the offside flag.
There was a consolation goal for the visiting fans to celebrate before the end, though, as Rogers showed a glimpse of why he is wanted by Premier League clubs by curling a late strike into the bottom corner with aplomb.
While the travelling supporters were determined to enjoy their trip to London, there was little else to smile about for Carrick and his players as Chelsea produced a statement victory to move within one match of a sixth League Cup crown, and a first since 2015.
The Blues will face either West London rivals Fulham or Liverpool, who beat them the last time they were in the final in 2022, at Wembley on February 25.