That growing confidence was perfectly illustrated by Kabangu when he received the ball on the edge of the area, controlled it well and curled a perfect shot into the far corner, leaving Internacional keeper Renan stranded.
Mazembe continued to live dangerously - with Kibiada constantly being called into action - but the Brazilian side could not break through.
A double substitution, with Tinga and Alecsandro being replaced by youngsters Giuliano and Damiao, gave Internacional more impetus, but they were unable to find an equaliser.
With five minutes remaining Kaluyituka sealed Mazembe's remarkable victory as he fired home a low shot from outside the area which beat Renan at the near post.
Mazembe will meet the winners of Wednesday's semi-final match between European Champions League winners Inter Milan of Italy or Seongnam Ilhwa of South Korea in Saturday's final.
Internacional will have to stay in Abu Dhabi to play the losers of that match-up in a play-off.
Their coach Celso Roth was philosophical about defeat at the hands of Mazembe.
"We controlled the game, but the best team is the one that wins," Roth said.
"It was time for Africa to reach the final and unfortunately it has been at our expense.
"There's no dishonour in that - African football is improving all the time and I don't see anything shameful in losing to an African team."
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