Trailing 3-1 in the second leg at Estadio Urbano Caldeira, Brazilian striker Willian struck the decisive away goal with nine minutes remaining.
And Willian put the result beyond doubt in the fifth minute of injury time as Cruzeiro claimed a 4-3 aggregate win against their top-flight opponents.
Needing to overturn a 1-0 first-leg deficit, Santos made a dream starting in front of their supporters on Wednesday.
Brazil international Robinho opened the scoring after just two minutes, driving into the penalty area before his shot took a deflection.
Cruzeiro were back on level terms six minutes later thanks to Bolivian Marcelo Moreno, who was on hand to tuck away a rebound from inside the six-yard box.
Gabriel's penalty in first-half stoppage time ensured Santos went into the break all square on aggregate with Cruzeiro after Rildo was brought down by Leo.
Santos moved ahead 3-2 on aggregate when Rildo completed a sweeping move from close range in the 58th minute.
But that is as good as it got for Santos, with Cruzeiro breaking their hearts during the closing stages.
Willian beat the offside trap before placing the ball beyond Santos goalkeeper Aranha nine minutes from time and he put the tie to bed in the 95th minute.
Cruzeiro - aiming to win a record-breaking fifth Copa do Brasil title - will face Atletico Mineiro in the decider.
Mineiro booked their spot in the final after triumphing 4-1 over Flamengo at Estadio Governador Magalhaes Pinto.
Levir Culpi's Mineiro lost the opening leg 2-0 but goals from Carlos, Maicosuel, Jesus Datolo and Luan gave the hosts a 4-3 win on aggregate.
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